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setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end /gnudict 256 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -33 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth } def /AL { stroke userlinewidth 2 div setlinewidth } def /UL { dup gnulinewidth mul /userlinewidth exch def 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end /gnudict 256 dict def gnudict begin /Color false def /Solid false def /gnulinewidth 5.000 def /userlinewidth gnulinewidth def /vshift -33 def /dl {10 mul} def /hpt_ 31.5 def /vpt_ 31.5 def /hpt hpt_ def /vpt vpt_ def /M {moveto} bind def /L {lineto} bind def /R {rmoveto} bind def /V {rlineto} bind def /vpt2 vpt 2 mul def /hpt2 hpt 2 mul def /Lshow { currentpoint stroke M 0 vshift R show } def /Rshow { currentpoint stroke M dup stringwidth pop neg vshift R show } def /Cshow { currentpoint stroke M dup stringwidth pop -2 div vshift R show } def /UP { dup vpt_ mul /vpt exch def hpt_ mul /hpt exch def /hpt2 hpt 2 mul def /vpt2 vpt 2 mul def } def /DL { Color {setrgbcolor Solid {pop []} if 0 setdash } {pop pop pop Solid {pop []} if 0 setdash} ifelse } def /BL { stroke userlinewidth 2 mul setlinewidth } def /AL { stroke userlinewidth 2 div setlinewidth } def /UL { dup gnulinewidth mul /userlinewidth exch def 10 mul /udl exch def } def /PL { stroke userlinewidth setlinewidth } def /LTb { BL [] 0 0 0 DL } def /LTa { AL [1 udl mul 2 udl mul] 0 setdash 0 0 0 setrgbcolor } def /LT0 { PL [] 1 0 0 DL } def /LT1 { PL [4 dl 2 dl] 0 1 0 DL } def /LT2 { PL [2 dl 3 dl] 0 0 1 DL } def /LT3 { PL [1 dl 1.5 dl] 1 0 1 DL } def /LT4 { PL [5 dl 2 dl 1 dl 2 dl] 0 1 1 DL } def /LT5 { PL [4 dl 3 dl 1 dl 3 dl] 1 1 0 DL } def /LT6 { PL [2 dl 2 dl 2 dl 4 dl] 0 0 0 DL } def /LT7 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 1 0.3 0 DL } def /LT8 { PL [2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 2 dl 4 dl] 0.5 0.5 0.5 DL } def /Pnt { stroke [] 0 setdash gsave 1 setlinecap M 0 0 V stroke grestore } def /Dia { stroke [] 0 setdash 2 copy vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke Pnt } def /Pls { stroke [] 0 setdash vpt sub M 0 vpt2 V currentpoint stroke M hpt neg vpt neg R hpt2 0 V stroke } def /Box { stroke [] 0 setdash 2 copy exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke Pnt } def /Crs { stroke [] 0 setdash exch hpt sub exch vpt add M hpt2 vpt2 neg V currentpoint stroke M hpt2 neg 0 R hpt2 vpt2 V stroke } def /TriU { stroke [] 0 setdash 2 copy vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C9 { BL [] 0 setdash 2 copy moveto 2 copy vpt 270 450 arc closepath fill vpt 0 360 arc closepath } bind def /C10 { BL [] 0 setdash 2 copy 2 copy moveto vpt 270 360 arc closepath fill 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C11 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill 2 copy moveto 2 copy vpt 270 360 arc closepath fill vpt 0 360 arc closepath } bind def /C12 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C13 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill 2 copy moveto 2 copy vpt 180 360 arc closepath fill vpt 0 360 arc closepath } bind def /C14 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 360 arc closepath fill vpt 0 360 arc } bind def /C15 { BL [] 0 setdash 2 copy vpt 0 360 arc closepath fill vpt 0 360 arc closepath } bind def /Rec { newpath 4 2 roll moveto 1 index 0 rlineto 0 exch rlineto neg 0 rlineto closepath } bind def /Square { dup Rec } bind def /Bsquare { vpt sub exch vpt sub exch vpt2 Square } bind def /S0 { BL [] 0 setdash 2 copy moveto 0 vpt rlineto BL Bsquare } bind def /S1 { BL [] 0 setdash 2 copy vpt Square fill Bsquare } bind def /S2 { BL [] 0 setdash 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S3 { BL [] 0 setdash 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S4 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S5 { BL [] 0 setdash 2 copy 2 copy vpt Square fill exch vpt sub exch vpt sub vpt Square fill Bsquare } bind def /S6 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill Bsquare } bind def /S7 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt vpt2 Rec fill 2 copy vpt Square fill Bsquare } bind def /S8 { BL [] 0 setdash 2 copy vpt sub vpt Square fill Bsquare } bind def /S9 { BL [] 0 setdash 2 copy vpt sub vpt vpt2 Rec fill Bsquare } bind def /S10 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S11 { BL [] 0 setdash 2 copy vpt sub vpt Square fill 2 copy exch vpt sub exch vpt2 vpt Rec fill Bsquare } bind def /S12 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill Bsquare } bind def /S13 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy vpt Square fill Bsquare } bind def /S14 { BL [] 0 setdash 2 copy exch vpt sub exch vpt sub vpt2 vpt Rec fill 2 copy exch vpt sub exch vpt Square fill Bsquare } bind def /S15 { BL [] 0 setdash 2 copy Bsquare fill Bsquare } bind def /D0 { gsave translate 45 rotate 0 0 S0 stroke grestore } bind def /D1 { gsave translate 45 rotate 0 0 S1 stroke grestore } bind def /D2 { gsave translate 45 rotate 0 0 S2 stroke grestore } bind def /D3 { gsave translate 45 rotate 0 0 S3 stroke grestore } bind def /D4 { gsave translate 45 rotate 0 0 S4 stroke grestore } bind def /D5 { gsave translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def end @fedspecial end TeXDict begin 39158280 55380996 1000 600 600 (main.dvi) @start /Fa 1 121 df<0007E001F000001FF807FC0000783E0E0F0000E01F1C1F0001C01F383F8003 800FF07F8003000FE0FF8007000FE0FF800E000FC0FF000C000FC07E000C001FC03C001C 001F80000018001F80000018001F80000000003F80000000003F80000000003F00000000 003F00000000007F00000000007F00000000007E00000000007E0000000000FE00000000 00FE0000000000FC000C000000FC000C000001FC001C001E01FC0018003F01F80018007F 81F80038007F83F8007000FF83F8006000FF07F800E000FE0E7C01C0007C1C7C03800078 383E0F00001FF00FFC000007C003F0000029267EA42F>120 D E /Fb 1 62 df<0000003000000078000000F8000000F8000000F0000001F0000001F00000 01E0000003E0000003E0000003C0000007C0000007C00000078000000F8000000F800000 0F0000001F0000001F0000003E0000003E0000003C0000007C0000007C00000078000000 F8000000F8000000F0000001F0000001F0000001E0000003E0000003E0000003C0000007 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b(af)c(o)o(v)o (erf\370rselshastighed)78 b(.)45 b(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f (.)125 b(11)727 2946 y(3.1.3)110 b(K)m(ompression)26 b(af)d(forbindelser)58 b(.)45 b(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g (.)g(.)g(.)h(.)f(.)125 b(13)518 3059 y(3.2)96 b(Udbyderne)27 b(.)45 b(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.) f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)125 b(13)727 3172 y(3.2.1)110 b(Unders\370gelse)27 b(af)c (datasammens\346tning)88 b(.)45 b(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f (.)125 b(14)518 3285 y(3.3)96 b(Sammenf)o(atning)60 b(.)45 b(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g (.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)125 b(15)382 3489 y FE(4)91 b(Inf)n(ormationsteori)2076 b(17)518 3601 y FJ(4.1)96 b(Entropi)88 b(.)46 b(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g (.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.) h(.)f(.)125 b(17)518 3714 y(4.2)96 b(Egenskaber)26 b(v)o(ed)e(entropi) 50 b(.)45 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b(fra)f(ordbogsbaserede)k (metoder)54 b(.)45 b(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.) 125 b(67)727 4841 y(A.2.1)89 b(Eksempel)25 b(fra)e(Lempel-Zi)n(v)h(78) 41 b(.)k(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)125 b(67)518 4954 y(A.3)75 b(Eksempler)25 b(fra)f(transformationer)41 b(.)k(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h (.)f(.)125 b(67)727 5067 y(A.3.1)89 b(Eksempel)25 b(fra)e(Burro)n (ws-Wheeler)77 b(.)45 b(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f (.)125 b(67)1854 5652 y(3)p eop %%Page: 4 6 4 5 bop 382 228 a FI(INDHOLD)p 382 266 2989 4 v 382 548 a FE(B)75 b(Beskri)o(v)o(else)26 b(af)d(unders\370gelser)1665 b(70)518 661 y FJ(B.1)80 b(T)-6 b(estsiderne)86 b(.)45 b(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g (.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)125 b(70)518 774 y(B.2)80 b(Datasammens\346tning)27 b(i)c(log\002ler)88 b(.)45 b(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.) h(.)f(.)125 b(71)727 887 y(B.2.1)94 b(Proxyserv)o(eren)27 b(granit.b)n(ut.auc.dk)74 b(.)45 b(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g (.)g(.)h(.)f(.)125 b(71)727 1000 y(B.2.2)94 b(IT)-8 b(-A)h(visen)52 b(.)46 b(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.) g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)125 b(72)518 1112 y(B.3)80 b(Ov)o(erf\370rselstid)27 b(for)d(forsk)o(ellige)i (forbindelser)71 b(.)45 b(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f (.)125 b(72)518 1225 y(B.4)80 b(T)-6 b(est)23 b(af)h(k)o (ompressionshastighe)q(d)70 b(.)45 b(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.) g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)125 b(73)382 1429 y FE(C)70 b(K)n(ompr)n(essionstest)2082 b(74)382 1633 y(D)70 b(Udbr)n(edelse)24 b(af)f(HTML-k)o(ompr)n(ession)1403 b(75)382 1837 y(E)75 b(T)-8 b(elef)n(oninter)o(views)2084 b(76)518 1950 y FJ(E.1)85 b(www)-6 b(.tv2.dk)53 b(.)45 b(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g (.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)125 b(76)518 2063 y(E.2)85 b(www)-6 b(.dating.dk)79 b(.)45 b(.)h(.)f(.)g(.)g(.)g(.)g (.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.) h(.)f(.)125 b(77)518 2176 y(E.3)85 b(www)-6 b(.o\002r)h(.dk)47 b(.)e(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)h(.)f(.)g (.)g(.)g(.)g(.)h(.)f(.)g(.)g(.)g(.)g(.)h(.)f(.)125 b(77)1854 5652 y(4)p eop %%Page: 5 7 5 6 bop 382 1171 a FC(Kapitel)43 b(1)382 1586 y FK(Indledning)382 2067 y FB(1.1)119 b(Pr)n(oblembeskri)o(v)o(else)382 2274 y FJ(Internet)38 b(er)f(v)o(erdens)h(hurtigst)g(v)n(oksende)i(medie)d (med)f(et)g(udb)n(ud)j(af)d(mange)h(milliarder)382 2387 y(websider)-5 b(.)34 b(Men)e(forbindelserne)38 b(til)32 b(internet)j(er)e(be)o(gr\346nset)h(i)e(b\345ndbredde,)k(dvs.)d(der)g (er)382 2500 y(gr\346nse)g(for)f(hv)n(or)h(me)o(get)f(data)h(der)f(kan) h(sendes)g(mellem)f(to)g(computere)i(pr)-5 b(.)32 b(sekund.)i(At)382 2613 y(k)o(\370be)j(ekstra)g(b\345ndbredde)i(er)d(relati)n(vt)i(dyrt)e (\226)g(dels)h(er)e(det)i(dyrt)f(for)h(virksomheder)i(der)382 2726 y(dri)n(v)o(er)23 b(websites,)h(og)f(dels)g(er)g(det)g(dyrt)g(for) g(brugerne.)i(Derfor)e(er)g(der)g(beho)o(v)h(for)f(at)f(udn)o(ytte)382 2839 y(disse)37 b(forbindelser)i(bedre,)e(og)f(det)h(er)f(her)g(k)o (ompression)j(k)o(ommer)d(ind)h(som)e(en)i(mulig)382 2952 y(l\370sning.)523 3065 y(K)m(ompression)c(handler)f(om)e(at)h(k)o (ode)h(data)f(for)g(derv)o(ed)h(at)e(formindsk)o(e)k(m\346ngden)d(af) 382 3178 y(dem)24 b(p\345)g(en)g(m\345de)h(s\345)f(de)g(kan)h (gendannes)i(n\345r)d(de)g(skal)h(bruges.)h(Denne)e(teknik)i(er)e (allerede)382 3290 y(me)o(get)h(udbredt)i(n\345r)e(det)g(g\346lder)h (billeder)l(,)h(lyd)e(og)g(\002lm,)e(men)i(ikk)o(e)h(for)f(HTML-sider)f (\(der)382 3403 y(er)f(de)g(\002ler)g(man)g(l\346ser)g(n\345r)h(man)f (surfer)h(p\345)g(internettet\))i(p\345)d(trods)i(af)e(at)g(disse)h (kan)g(k)o(ompri-)382 3516 y(meres)d(me)o(get)g(ef)n(fekti)n(vt.)i(Men) d(hv)n(orfor)k(bli)n(v)o(er)d(siderne)i(s\345)e(ikk)o(e)h(k)o (omprimeret?)h(Det)e(kunne)382 3629 y(v\346re)k(fordi)g(HTML-\002lerne) f(udg\370r)i(en)f(for)g(lille)g(del)g(af)g(tra\002kk)o(en)h(til)f(at)f (det)h(kan)h(betale)g(sig)382 3742 y(at)d(bruge)i(k)o(ompression)h (p\345)e(dem.)523 3855 y(Hvis)g(man)f(skal)i(k)o(omprimere)g (HTML-\002ler)l(,)d(hvilk)o(en)k(algoritme)g(skal)e(man)g(s\345)f (bruge?)382 3968 y(Det)29 b(kan)i(ikk)o(e)g(v\346re)f(en)g(af)g(de)g (ellers)h(me)o(get)f(ef)n(fekti)n(v)o(e)h(algoritmer)h(med)e(tab,)g (som)g(inde-)382 4081 y(b\346rer)d(at)f(\002lerne)h(ikk)o(e)g(kan)h (genskabes)h(til)d(n\370jagtigt)j(det)e(samme)g(som)f(f\370r)h(k)o (ompression;)382 4194 y(i)d(mods\346tning)i(til)e(billeder)i(og)e(lyd)h (kan)f(man)g(nemlig)h(v)o(ed)g(HTML-sider)f(ikk)o(e)h(tillade)g(\346n-) 382 4307 y(dringer)l(,)g(da)f(dette)g(kunne)h(la)n(v)o(e)f(om)f(p\345)h (layout)h(og)e(mening)i(for)e(udbydernes)k(websider)-5 b(.)523 4420 y(Men)27 b(der)h(\002ndes)g(stadig)g(mange)g(algoritmer)i (der)d(er)g(tabsfri.)i(Hvilk)o(en)f(skal)h(vi)e(v\346lge,)382 4532 y(og)33 b(hvis)i(vi)e(endelig)i(\002nder)f(en)f(algoritme,)i (\002ndes)f(der)g(s\345)f(de)h(teknisk)o(e)h(foruds\346tninger)382 4645 y(til)25 b(at)g(l\370sningen)j(kan)e(implementeres?)i(Kan)d(man)g (o)o(v)o(erho)o(v)o(edet)i(f\345)e(folk)h(til)g(at)f(bruge)h(det?)382 4758 y(Dette)32 b(afh\346nger)h(selvf\370lgelig)i(af)c(hv)n(or)i(stor)f (en)f(e)n(vt.)h(besparelse)i(ville)e(v\346re,)f(hv)n(or)i(godt)382 4871 y(teknologien)23 b(kunne)d(inte)o(greres)i(med)d(eksisterende)j (praksis)f(og)f(hv)n(orvidt)h(den)f(n\370dv)o(endige)382 4984 y(viden)25 b(er)e(til)h(stede)h(hos)f(udbyderne)j(af)c(disse)i (websider)l(,)g(men)e(dette)i(er)e(alle)i(sp\370r)n(gsm\345l)h(der)382 5097 y(bli)n(v)o(er)e(diskuteret)i(i)d(rapporten.)1854 5652 y(5)p eop %%Page: 6 8 6 7 bop 1487 228 a FI(Kapitel)25 b(1:)e(Indledning)p 382 266 2989 4 v 382 548 a FB(1.2)119 b(Pr)n(oblemf)m(ormulering)382 755 y FJ(Problemet)24 b(er)f(alts\345)h(om)f(det)g(er)g(en)g(fordel)i (at)e(indf\370re)i(k)o(ompression)h(af)d(HTML-sider)g(o)o(v)o(er)382 868 y(internettet)40 b(for)d(brugere)i(og)f(udbydere,)h(og)e(hvilk)o (en)j(metode)e(man)e(i)h(gi)n(v)o(et)h(f)o(ald)g(skulle)382 981 y(bruge.)382 1273 y FB(1.3)119 b(Ov)o(ersigt)29 b(o)o(v)o(er)g(pr)n (ojektet)382 1480 y FJ(V)-5 b(i)17 b(starter)i(med)f(at)g(unders\370ge) j(hv)n(ad)e(k)o(ompression)i(af)d(data)h(er)f(for)h(noget)g(for)f(at)g (f\345)g(opbygget)382 1593 y(en)28 b(f)o(ast)i(referenceramme)h(til)e (resten)g(af)g(rapporten.)i(Herefter)e(behandler)i(vi)e(sp\370r)n (gsm\345let)382 1706 y(om)e(det)h(o)o(v)o(erho)o(v)o(edet)i(kan)e (betale)h(sig)f(at)f(indf\370re)j(k)o(ompression)g(af)e(websider)h (\226)e(bl.a.)h(un-)382 1819 y(ders\370ger)34 b(vi)e(for)h(de)f(to)g (ho)o(v)o(edparter)l(,)j(brugerne)f(og)f(udbyderne,)i(hv)n(or)e(stor)f (en)h(m\346ngde)382 1932 y(data)23 b(HTML-siderne)g(udg\370r)g(i)f (forhold)i(til)e(den)h(totale)g(m\346ngde)g(data)g(der)f(o)o(v)o (erf\370res,)i(dette)382 2045 y(inkluderer)30 b(bla.)d(billeder)h(og)g (lyd.)f(Dette)g(kan,)g(ud)g(o)o(v)o(er)g(at)g(indik)o(ere)i(i)d(hv)n (or)i(stor)g(udstr\346k-)382 2158 y(ning)23 b(det)f(er)g(rele)n(v)n (ant)i(at)e(k)o(omprimere)i(HTML-\002ler)l(,)c(gi)n(v)o(e)j(en)f (baggrund)j(for)d(at)g(vurdere)i(de)382 2271 y(algoritmer)h(vi)f (senere)h(analyserer)-5 b(.)523 2384 y(Herefter)28 b(k)o(ommer)e(vi)h (ind)g(p\345)f(informationsteori)31 b(som)26 b(gi)n(v)o(er)h(en)g (teoretisk)h(forst\345else)382 2497 y(for)c(og)f(et)h(o)o(v)o(erblik)h (o)o(v)o(er)e(hv)n(orfor)j(k)o(ompressionsalgoritmer)j(virk)o(er)-5 b(.)523 2609 y(Denne)25 b(forst\345else)j(s\346tter)d(os)g(i)f(stand)i (til)f(at)g(foretage)i(en)d(unders\370gelse)29 b(af)c(forsk)o(ellige) 382 2722 y(algoritmer)32 b(\226)e(dette)h(resulterer)i(i)c(en)i (analyse)h(og)e(sammenligning)j(af)d(forsk)o(ellige)k(m\345der)382 2835 y(at)25 b(k)o(omprimere)h(p\345)f(og)g(en)g(afv)o(ejning)i(af)e (deres)h(styrk)o(er)g(og)f(sv)n(agheder)j(i)c(forbindelse)k(med)382 2948 y(websidek)o(ompression.)35 b(Sammen)29 b(med)h(de)g(resultater)i (vi)e(har)h(opn\345et)g(v)o(ed)f(beho)o(vsanaly-)382 3061 y(sen,)d(fors\370ger)i(vi)e(derefter)h(at)f(vurdere)i(en)e (alternati)n(v)i(metode)e(til)g(at)g(opn\345)h(bedre)g(k)o(ompri-)382 3174 y(mering)21 b(af)g(websider)-5 b(.)22 b(Dette)f(f\370lges)h(op)f (af)f(en)h(implementation)j(der)d(tillader)h(os)f(at)g(foretage)382 3287 y(en)i(test)h(der)g(kan)g(holdes)h(op)f(mod)f(g\346ngse)i(k)o (omprimeringsmetoder)j(som)23 b FA(gzip)f FJ([10)q(].)523 3400 y(V)-12 b(ores)20 b(praktisk)o(e)j(test)d(gi)n(v)o(er)g(desuden)i (et)d(grundlag)j(for)e(at)g(besv)n(are)h(sp\370r)n(gsm\345let)i(om)c (de)382 3513 y(kra)n(v)g(som)g(brugerne)i(og)e(udbyderne)i(m\345tte)e (stille)h(til)e(en)h(k)o(ompressionsl\370sning)q(,)k(kan)d(opfyl-)382 3626 y(des,)25 b(og)h(kan)g(derfor)h(hj\346lpe)f(med)f(at)g(afklare)i (om)e(en)g(k)o(ompressionsl\370snin)q(g)31 b(o)o(v)o(erho)o(v)o(edet) 382 3739 y(vil)d(ha)n(v)o(e)h(nogen)h(chance)g(for)e(bli)n(v)o(e)h(an)l (v)o(endt)h(hos)f(henholdsvis)i(brugerne)g(og)d(udbyderne.)382 3851 y(Sidste)c(del)g(af)f(rapporten)j(behandler)g(dette)f(emne.)523 3964 y(Men)e(vi)h(starter)h(med)e(en)h(grundl\346ggende)j (unders\370gelse)g(af)d(k)o(ompression.)1854 5652 y(6)p eop %%Page: 7 9 7 8 bop 382 1171 a FC(Kapitel)43 b(2)382 1586 y FK(Intr)l(oduktion)52 b(til)g(k)m(ompr)l(ession)382 2031 y FJ(Der)21 b(er)h(forsk)o(el)i (p\345)e(st\370rrelsen)i(af)e(en)g(datam\346ngde)i(og)e(st\370rrelsen)j (af)c(informationsindhol-)382 2144 y(det)27 b(i)g(dataene.)h(At)e FD(k)o(omprimer)m(e)j FJ(handler)f(om)f(at)g(formindsk)o(e)i (st\370rrelsen)h(af)c(data)i(uden)g(at)382 2257 y(\370del\346gge)d (informationsindhold)q(et.)523 2369 y(I)20 b(rapporten)j(opf)o(atter)g (vi)d(data)h(som)g(best\345ende)i(af)d(en)h(ordnet)h(r\346kk)o(e)f(af)f FD(symboler)p FJ(,)i(eller)382 2482 y FD(te)l(gn)p FJ(,)30 b(der)f(via)h(en)f(k)o(ompressionsalgoritme)34 b(gennemg\345r)e(en)d FD(k)o(odning)i FJ(s\345)e(de)g(bli)n(v)o(er)h(til)f(en)382 2595 y(ordnet)23 b(r\346kk)o(e)f(af)f FD(k)o(odeor)m(d)p FJ(,)i(eller)f(bare)g(k)o(oder)l(,)g(der)g(gerne)g(samlet)g(skulle)h (v\346re)e(mindre)h(end)382 2708 y(den)i(oprindelige)j(r\346kk)o(e.)523 2821 y(Grunden)d(til)e(at)g(man)h(kan)f(k)o(omprimere,)i(h\346nger)f (dels)g(sammen)g(med)f(at)g(man)h(ofte)g(har)382 2934 y(data)k(liggende)i(i)c(en)i(form)f(som)g(g\370r)h(at)f(det)h(er)f (hurtigere)i(og/eller)h(lettere)e(at)g(bruge)g(dem)f(\226)382 3047 y(f.eks.)j(bruger)i(man)d(som)h(re)o(gel)h(8)e(bit)i(til)f(at)g (repr\346sentere)i(te)o(gn,)e(ogs\345)h(selv)n(om)g(man)f(reelt)382 3160 y(kun)24 b(bruger)h(m\345sk)o(e)f(128)g(forsk)o(ellige)j(te)o(gn)d (som)f(kunne)i(lagres)g(p\345)e(7)g(bit.)h(Dels)f(h\346nger)i(det)382 3273 y(sammen)h(med)g(at)g(de)g(data)g(vi)g(almindeligvis)j (besk\346ftiger)g(os)d(med,)f(f.eks.)h(tekst,)h(normalt)382 3386 y(fylder)e(mere)e(end)h(den)g(information)i(de)e(viderebringer)j (\226)c(der)h(er)g FD(r)m(edundans)i FJ(i)d(dem.)523 3499 y(Den)28 b(f\370rste)h(type)g(af)f(o)o(v)o(er\003\370digt)i(data)f (som)f(beskre)n(v)o(et)i(i)e(o)o(v)o(enst\345ende)j(er)d(relati)n(vt)i (let)382 3611 y(at)j(sk\346re)g(v\346k)f(da)h(det)g(blot)h(kr\346v)o (er)f(at)f(man)h(i)f(stedet)i(for)f(at)g(optimere)h(mht.)f(hastighed,) 382 3724 y(g\345r)24 b(o)o(v)o(er)f(til)g(at)g(opbe)n(v)n(are)i (dataene)h(mere)d(k)o(ompakt.)h(F)-7 b(.eks.)23 b(kunne)h(modtager)h (og)f(afsender)382 3837 y(enes)32 b(om)f(at)h(bruge)g(en)g FD(or)m(dbo)o(g)p FJ(,)h(en)e(forte)o(gnelse)k(o)o(v)o(er)c(symboler)i (med)e(deres)i(tilh\370rende)382 3950 y(k)o(odeord,)e(hv)n(or)f(der)g (kun)f(optr\346der)i(de)e(te)o(gn)g(der)h(f)o(aktisk)h(bruges)f(s\345)f (man)g(kun)h(beh\370)o(v)o(ede)382 4063 y(f.eks.)24 b(5)f(bit)g(til)h (at)f(repr\346sentere)k(et)c(te)o(gn.)523 4176 y(Det)28 b(er)h(imidlertid)i(sv\346rere)f(at)f(k)o(omme)g(redundansen)k(i)28 b(dataene)j(til)e(li)n(vs)g(\226)g(man)f(kan)382 4289 y(grundl\346ggende)i(g\345)c(to)g(v)o(eje:)h(enten)h(kan)e(man)h (v\346lge)f(en)h(generel)h(metode,)e(som)g(en)h(af)f(de)382 4402 y(der)21 b(er)f(beskre)n(v)o(et)i(i)e(kapitel)i(5,)e(eller)h(en)f (metode)i(som)e(er)g(optimeret)i(til)f(netop)g(den)g(type)g(data)382 4515 y(man)e(arbejder)j(med.)d(En)g(unders\370gelse)24 b(af)19 b(dataene)j(gi)n(v)o(er)e(naturligvis)j(mulighed)e(for)f(bedre) 382 4628 y(k)o(ompression)25 b(og)d(oftest)i(sk)o(er)f(der)f(ogs\345)h (en)g(analyse)h(af)e(de)g(data)h(der)f(\370nsk)o(es)i(k)o(omprimeret,) 382 4741 y(inden)h(den)f(reelle)g(k)o(ompression)j(igangs\346ttes,)e (ogs\345)f(v)o(ed)g(de)g(generelle)h(metoder)-5 b(.)523 4853 y(En)28 b(uddybning)j(og)e(forklaring)i(af)d (redundansf\346nomenet)33 b(gi)n(v)o(es)c(i)f(kapitel)i(4,)e(men)g(et) 382 4966 y(k)o(ort)c(eksempel)h(med)f(sekv)o(ensl\346ngdek)o(odning)29 b(kan)24 b(illustrere)i(det.)523 5079 y(Sekv)o(ensl\346ngdek)o(odning)j (eller)24 b(\204run)g(length)g(encoding\223,)i(RLE,)21 b(g\345r)j(ud)f(p\345)g(at)g(erstatte)382 5192 y(gentagelser)33 b(af)d(samme)f(symbol)i(med)f(et)f(enk)o(elt)i(symbol)g(samt)f (antallet)i(af)d(forek)o(omster)382 5305 y(\226)d(f.eks.)g(kan)h (\204muuuuuuuuh\223)j(erstattes)e(med)e(\204m*8uh\223)i(hv)n(or)f (stjernen)h(repr\346senterer)h(et)1854 5652 y(7)p eop %%Page: 8 10 8 9 bop 1165 228 a FI(Kapitel)24 b(2:)f(Introduktion)28 b(til)23 b(k)o(ompression)p 382 266 2989 4 v 382 548 a FJ(k)o(ontrolte)o(gn)j(som)d(bruges)i(v)o(ed)e(afk)o(odningen)k(til)c (at)g(afg\370re)i(at)e(n\346ste)g(te)o(gn)h(skal)g(duplik)o(eres)382 661 y(et)32 b(antal)h(gange.)g(Dette)f(nedbringer)j(datam\346ngden)f (fra)f(10)f(til)g(5)g(te)o(gn,)g(dvs.)g(gi)n(v)o(er)h FD(k)o(om-)382 774 y(pr)m(essionsforholdet)k FJ(50\045)30 b(\(k)o(ompressionsforhold)36 b(er)30 b(de\002neret)h(som)f(forholdet)i (mellem)382 887 y(st\370rrelsen)24 b(af)c(de)i(k)o(omprimerede)h(data)f (og)f(st\370rrelsen)j(af)d(de)g(oprindelige)j(data,)d(f.eks.)h(1:2\).) 382 1000 y(Dette)k(forhold)j(er)d(naturligvis)j(ikk)o(e)e(generelt)i (for)d(RLE)f(som)h(ikk)o(e)h(er)f(s\346rligt)h(v)o(ele)o(gnet)h(til)382 1112 y(at)23 b(k)o(omprimere)i(almindelig)h(tekst,)e(men)g(kan)g (v\346re)f(ef)n(fekti)n(v)i(i)e(andre)i(sammenh\346nge.)523 1225 y(Det)e(skal)g(i)g(\370)o(vrigt)h(bem\346rk)o(es)g(at)f(de)g (generelle)i(algoritmer)g(ikk)o(e)f(er)f(s\345)g(generelle)i(at)e(de) 382 1338 y(kan)c(k)o(omprimere)i FD(alle)f(typer)i FJ(data)d(\226)g(k)o (ompression)j(kan)d(jo)g(betragtes)j(som)c(en)h(funktion)j(der)382 1451 y(afbilder)i(en)e(gi)n(v)o(en)h(m\346ngde)f(data)h(o)o(v)o(er)f(i) g(en)g(v\346rdim\346ngde.)i(Funktionen)g(skal)f(imidlertid)382 1564 y(v\346re)35 b(en)h(bijektion)i(hvis)e(man)g(altid)g(skal)g(kunne) h(k)o(omme)f(tilbage)h(til)f(de)f(samme)h(data,)382 1677 y(hv)n(orfor)e(v\346rdim\346ngden)g(skal)f(v\346re)f(lige)h(s\345)f (stor)h(som)f(de\002nitionsm\346ngden)j(hvis)e(alle)382 1790 y(elementer)38 b(i)e(de\002nitionsm\346ngden)k(kan)d(forek)o(omme) h(i)e(dataene.)i(Alts\345)f(kan)g(man)f(ikk)o(e)382 1903 y(generelt)25 b(g\345)f(fra)g(f.eks.)f(8)g(bit)h(til)g(7,)f(ikk)o(e)h (alle)g(data)g(kan)g(k)o(omprimeres.)523 2016 y(I)j(nogle)i (tilf\346lde)g(af)e(k)o(ompression)k(kan)d(man)g(tillade)h(et)e(tab)h (af)g(data)g(s\345)g(k)o(ompression)382 2129 y(fulgt)22 b(af)g(dek)o(ompression)j(ikk)o(e)d(gi)n(v)o(er)g(pr\346cist)g(de)f (samme)h(data.)f(Dette)h(sk)o(er)g(ofte)g(v)o(ed)g(k)o(om-)382 2242 y(pression)31 b(af)d(lyd)i(eller)f(billeder)i(som)d(man)h(som)f (re)o(gel)h(kan)h(beskri)n(v)o(e)g(med)e(f\346rre)h(detaljer)382 2355 y(og)j(nuancer)j(uden)e(at)g(det)f(beh\370)o(v)o(er)i(at)e (v\346re)h(m\346rkbart.)g(Derv)o(ed)g(reducerer)h(man)f(antal-)382 2467 y(let)e(af)g(forsk)o(ellige)k(te)o(gn)c(s\345)h(der)f(kan)h (opn\345s)h(en)e(bedre)h(k)o(ompression;)j(JPEG)29 b(og)j(MP3)e(er)382 2580 y(eksempler)25 b(p\345)f(dette.)523 2693 y(Som)e(tidligere)k (n\346vnt)e(vil)f(vi)g(dog)h(i)f(denne)i(rapport)g(besk\346ftige)g(os)f (med)f(tabsfri)i(k)o(om-)382 2806 y(pression)20 b(fordi)g(udseendet)h (og)d(indholdet)k(af)c(siderne)i(ikk)o(e)f(m\345)f(bli)n(v)o(e)h (forstyrret.)h(Der)e(er)g(dog)382 2919 y(to)26 b(sider)h(af)f(HTML)e (\226)i(det)h(indhold)h(som)e(f.eks.)g(forf)o(atteren)j(af)e (dokumentet)h(ser)l(,)f(k)o(oderne)382 3032 y(og)34 b(teksten,)i(og)e (den)h(formaterede)i(fremstilling)f(som)e(brugerne)j(af)d(siderne)i (ser)e(i)g(deres)382 3145 y(bro)n(wser)-5 b(.)25 b(Man)f(kan)g(ar)n (gumentere)j(for)e(at)f(sm\345)f(\346ndringer)j(i)e(HTML-k)o(oderne,)h (f.eks.)f(skift)382 3258 y(fra)30 b(sm\345)f(bogsta)n(v)o(er)j(til)d (store,)i(der)f(ikk)o(e)g(gi)n(v)o(er)g(nogen)h(forsk)o(el)g(i)e (udseendet)k(i)c(bro)n(wseren,)382 3371 y(ikk)o(e)24 b(medf\370rer)h(noget)g(tab)l(.)f(V)-5 b(i)22 b(o)o(v)o(erv)o(ejer)j (dette)f(i)f(kapitel)j(6.)523 3484 y(Efter)g(denne)h(k)o(orte)g (introduktion)i(til)d(k)o(omprimeringsbe)o(grebet)31 b(f\370lger)d(en)d(analyse)j(af)382 3597 y(beho)o(v)o(et)d(for)e(en)h (k)o(ompression)i(af)e(websider)-5 b(.)1854 5652 y(8)p eop %%Page: 9 11 9 10 bop 382 1171 a FC(Kapitel)43 b(3)382 1586 y FK(Beho)n(vsanalyse) 382 2031 y FJ(Udgangspunktet)29 b(for)c(denne)i(rapport)g(er)e(at)g(k)o (ompression)j(af)d(websider)i(har)e(et)g(potentiale)382 2144 y(for)e(udbredelse.)j(Men)e(hv)n(ad)g(best\345r)g(potentialet)j(e) o(gentligt)e(af,)e(og)g(hv)o(em)g(g\346lder)h(det?)g(F)o(or)n(-)382 2257 y(m\345let)c(med)g(beho)o(vsanalysen)k(er)c(at)g(f\345)g(klarlagt) i(disse)f(sp\370r)n(gsm\345l)h(\226)e(is\346r)g(er)g(det)g(interessant) 382 2369 y(om)j(et)g(e)n(vt.)g(beho)o(v)i(er)e(stort)i(nok)f(til)f(at)h (kunne)h(moti)n(v)o(ere)f(en)f(almen)h(brug.)523 2482 y(Man)29 b(kan)g(sk)o(elne)h(mellem)e(to)h(parter:)h(de)f(almindelige)i (brugere)f(af)f(websider)h(og)f(ud-)382 2595 y(byderne,)36 b(dem)e(der)g(ejer)h(og)f(dri)n(v)o(er)h(de)g(foresk)o(ellige)i (websites.)f(Den)e(f\370lgende)i(analyse)382 2708 y(fokuserer)24 b(p\345)d(teknisk)o(e)j(problemer)f(\226)e(problemer)i(som)f(brugerv)o (enlighed)k(og)21 b(\370k)o(onomisk)o(e)382 2821 y(forhold)j(i)e (forbindelse)k(med)c(at)h(indf\370re)h(en)e(l\370sning)j(ude)e(i)f (erhv)o(ervsli)n(v)o(et)j(bli)n(v)o(er)e(behandlet)382 2934 y(i)g(kapitel)i(8.)382 3227 y FB(3.1)119 b(Bruger)n(ne)382 3434 y FJ(F)o(or)30 b(brugerne)i(er)f(det)g(mest)f(af)g(alt)h(et)f (sp\370r)n(gsm\345l)j(om)d(at)g(k)o(omprimerede)j(sider)f(kan)f(gi)n(v) o(e)382 3547 y(en)26 b(hastighedsge)n(vinst)31 b(\226)25 b(ogs\345)i(rent)f(\370k)o(onomisk)i(er)e(selv)o(e)g (tra\002km\346ngden)h(ikk)o(e)g(s\345)f(inter)n(-)382 3659 y(essant)h(fordi)f(man)f(som)g(oftest)i(betaler)g(pr)-5 b(.)25 b(tid)g(og)h(ikk)o(e)g(pr)-5 b(.)25 b(kb)h(hentet)g(data)2850 3626 y Fz(1)2889 3659 y FJ(.)e(Hastigheds-)382 3772 y(forbedringen)j (kan)e(dels)f(k)o(omme)g(direkte)h(v)o(ed)f(at)g(mindre)g(\002ler)f (tager)i(k)o(ortere)h(tid)d(at)h(hente,)382 3885 y(dels)j(indirekte)i (v)o(ed)e(at)f(en)h(generelt)h(mindre)f(tra\002km\346ngde)h(p\345)f (internettet)i(alt)e(andet)g(lige)382 3998 y(b)n(urde)e(gi)n(v)o(e)f(k) o(ortere)i(responstider)i(for)c(alle.)g(Sidstn\346vnte)i(er)d(dog)i(i)e (sagens)j(natur)f(sv\346rt)f(at)382 4111 y(unders\370ge,)i(og)e(vi)f (besk\346ftiger)j(os)e(i)f(det)g(f\370lgende)j(kun)e(med)g(den)g (umiddelbare)i(ge)n(vinst.)523 4224 y(Hastighedsge)n(vinsten)33 b(afh\346nger)c(naturligvis)h(af)d(k)o(omprimeringsalgoritmen)33 b(\226)27 b(dels)382 4337 y(hv)n(or)d(ef)n(fekti)n(vt)h(den)f(k)o (omprimerer)l(,)h(dels)f(hv)n(or)g(hurtig)h(den)e(er)-5 b(.)23 b(Ge)n(vinsten)i(afh\346nger)g(imid-)382 4450 y(lertid)g(ogs\345)f(af)g(HTML-dataenes)h(andel)f(af)g(den)g(samlede)h (o)o(v)o(erf\370rte)g(m\346ngde)f(data)h(\226)e(hvis)382 4563 y(f.eks.)29 b(kun)g(1\045)f(af)g(dataene)j(er)d(HTML,)e(vil)j(en)g (k)o(ompressionsl\370sning)q(,)k(lige)o(gyldigt)f(hv)n(or)382 4676 y(ef)n(fekti)n(v)25 b(den)f(er)l(,)f(n\346ppe)h(v\346re)g (interessant)i(fordi)f(den)f(mulige)g(ge)n(vinst)h(er)f(for)f(lille.) 523 4789 y(Desuden)f(skal)f(en)g(hastighedsge)n(vinst)26 b(i)20 b(forbindelse)k(med)c(o)o(v)o(erf\370rslerne)k(s\346ttes)d(i)f (for)n(-)382 4901 y(hold)26 b(til)f(hv)n(or)i(lang)f(tid)f(det)h(tager) g(at)f(o)o(v)o(erf\370re)h(dataene)i(nu.)d(Selv)n(om)g(den)h(relati)n (v)o(e)g(ge)n(vinst)382 5014 y(kan)31 b(v\346re)f(stor)l(,)i(f.eks.)e (50\045,)g(ville)i(det)f(ikk)o(e)g(betyde)h(noget)g(hvis)f(en)g(gi)n(v) o(en)g(bruger)h(sam-)382 5127 y(menlagt)25 b(kun)f(sparede)h(en)f (hundredel)i(sekund.)p 382 5208 1196 4 v 487 5264 a Fy(1)516 5296 y Fx(Dog)20 b(med)f(enk)o(elte)h(undtagelser)m(,)g(heriblandt)f (Stof)o(aNet)1854 5652 y FJ(9)p eop %%Page: 10 12 10 11 bop 1412 228 a FI(Kapitel)25 b(3:)e(Beho)o(vsanalyse)p 382 266 2989 4 v 523 548 a FJ(I)e(be)o(gge)h(tilf\346lde)h(ville)f(der) g(ikk)o(e)g(v\346re)f(beho)o(v)h(for)g(en)f(l\370sning.)i(V)-5 b(i)21 b(er)g(derfor)h(n\370dt)h(til)e(at)382 661 y(foretage)g(en)d (unders\370gelse)23 b(af)18 b(dels)i(HTML-\002lernes)e(andel)i(af)e (den)i(samlede)f(datam\346ngde,)382 774 y(dels)24 b(af)f(de)h (nuv\346rende)i(o)o(v)o(erf\370rselstider)-5 b(.)382 1023 y Fw(3.1.1)99 b(Unders\370gelse)25 b(af)g(datasammens\346tning)382 1197 y FJ(T)m(il)h(analysen)j(betragter)h(vi)c(en)h(log\002l)h(for)f (proxyserv)o(eren)k Fv(granit.but.auc)o(.d)o(k)p FJ(,)20 b(en)382 1310 y(maskine)i(der)f(sidder)h(mellem)e(de)h(lokale)h (brugere)g(p\345)f(basisuddannelsen)26 b(p\345)21 b(Aalbor)n(g)h(Uni-) 382 1423 y(v)o(ersitet,)j(og)e(resten)i(af)e(internettet)k(og)c(gemmer) h(ofte)g(ben)o(yttede)i(\002ler)d(midlertidigt.)523 1536 y(Log\002len)31 b(indeholder)j(oplysninger)g(om)c(hvilk)o(e)i(\002ler)e (p\345)h(internettet)i(brugere)g(p\345)e(ba-)382 1649 y(sisuddannelsen)k(har)30 b(bes\370gt,)h(og)f(en)g(analyse)i(af)e(den)h (kan)f(derfor)h(gi)n(v)o(e)g(et)e(o)o(v)o(erblik)j(o)o(v)o(er)382 1762 y(omkring)h(900)f(mennesk)o(ers)j(dataforbrug,)g(se)c(tabel)i(3.1) f(\(selv)o(e)h(analyseprogrammet)j(og)382 1875 y(sorteringskriteriern)q (e)27 b(er)22 b(beskre)n(v)o(et)i(i)e(afsnit)h(B.2\).)e(Der)h(er)g(dog) g(ingen)i(garanti)f(for)f(at)g(data-)382 1988 y(forbruget)j(fra)d (maskiner)h(p\345)g(uni)n(v)o(ersitetet)i(modsv)n(arer)f (forbrugsm\370nstret)i(n\345r)d(folk)g(sidder)382 2101 y(hjemme.)g(Dette)h(antager)h(vi)f(dog.)p 643 2227 2468 8 v 692 2332 a(datatype)149 b(m\346ngde)23 b(\(Mb\))101 b(andel)24 b(\(\045\))100 b(i)23 b(cache)i(\(\045\))100 b(st\370r)-5 b(.)24 b(\(kb\))p 643 2386 2468 5 v 692 2490 a(HTML)306 b(1879,37)289 b(11,69)281 b(15,16)290 b(7,79)692 2603 y(billeder)g(1622,76)f(10,09)304 b(61,6)312 b(6,62)692 2716 y(andet)347 b(12580,49)267 b(78,22)304 b(2,19)290 b(27,02)p 643 2770 V 692 2874 a(statisk)357 b(364,45)312 b(19,39)281 b(41,18)290 b(9,71)692 2987 y(dynamisk)214 b(1514,92)289 b(80,61)327 b(8,9)334 b(7,44)p 643 3044 2468 8 v 590 3223 a FD(T)-8 b(abel)23 b(3.1:)31 b(T)-8 b(abel)24 b(o)o(ver)g(en)g(ug)o(es)g(tr)o(a\002k)h(fr)o(a)e (basisuddannelsens)30 b(pr)l(oxyserver)382 3567 y FE(F)n(ordelingen)23 b(af)h(datam\346ngden)382 3741 y FJ(T)-7 b(abel)18 b(3.1)g(gi)n(v)o(er) g(oplysninger)k(om)17 b(tre)i(forsk)o(ellige)i(kate)o(goriers)g(andel)e (af)f(tra\002kk)o(en,)h(HTML)382 3854 y(som)29 b(er)h(de)g(websider)h (vi)f(kunne)h(v\346re)f(interesseret)j(i)c(at)g(k)o(omprimere,)j (billeder)f(der)f(ofte)382 3967 y(indg\345r)35 b(som)f(en)g(del)g(af)g (siderne,)i(men)d(ligger)j(s\346rskilt)f(og)f(s\345)g(godt)g(som)g (altid)h(er)f(k)o(om-)382 4080 y(primerede,)e(og)e(andet)h(der)g (d\346kk)o(er)g(o)o(v)o(er)f(65\045)h(programdata)h(\(n\346sten)g (udelukk)o(ende)i(fra)382 4193 y Fv(distributed.net)o FJ(-klienter)1511 4160 y Fz(2)1545 4193 y FJ(\),)26 b(4\045)h(lyd,)f (7\045)h(video)h(og)f(24\045)f(andre)i(ting)f(som)g(ISO-)382 4306 y(\002ler)c(\(til)h(cd'ere\),)h(programmer)g(og)e(andre)i(pakk)o (ede)h(ting.)523 4419 y(Umiddelbart)40 b(gi)n(v)o(er)f(fordelingen)i 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Fx(Program)19 b(der)h(arbejder)f(i)f(baggrunden)k(og)d(l\370ser)g(sv\346re)g (problemer)h(fra)f(en)g(central)g(serv)o(er)1831 5652 y FJ(10)p eop %%Page: 11 13 11 12 bop 1412 228 a FI(Kapitel)25 b(3:)e(Beho)o(vsanalyse)p 382 266 2989 4 v 382 548 a FJ(fordelingen)36 b(v\346re)d(noget)h (sk\346v)g(i)e(retning)j(af)e(de)g(78\045)g(andre)h(data)g(fordi)g(uni) n(v)o(ersitetets)382 661 y(internetforbindelse)d(er)25 b(me)o(get)g(hurtigere)i(end)f(de)f(\003estes)h(brugers)g(linjer)l(,)h (100)e(Mbit/s,)h(og)382 774 y(dermed)e(bedre)h(er)e(i)g(stand)i(til)e (at)h(klare)g(de)g(tunge)h(datatyper)-5 b(.)523 887 y(En)18 b(sidste)i(pointe)f(er)g(at)f(de)h(datam\346ngder)h(der)f(er)f(angi)n (v)o(et)i(i)e(tabellen,)i(er)e(for)h(de)g(f)o(aktisk)o(e)382 1000 y(o)o(v)o(erf\370rsler)25 b(mellem)f(proxyserv)o(eren)j(og)c (internettet)j(\226)d(k)o(olonnen)j(med)d(\204i)g(cache\223)i(viser)f (at)382 1112 y(f.eks.)k(billeder)h(ofte)f(kan)g(hentes)h(fra)f 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b(allerede)e(omkring)f(2)e(sekunders)k(v)o(entetid)f(kan)e(m\346rk)o (es.)g(I)g(hv)o(ert)g(f)o(ald)h(er)382 4581 y(5-10)29 b(sekunders)j(v)o(entetid)e(for)f(de)g(middelstore)i(sider)e(med)g(det) g(analoge)h(modem)f(nok)g(til)382 4694 y(at)35 b(kunne)h(forstyrre,)g (og)f(if\370lge)i([19)q(])d(er)h(der)g(2,8)f(mill.)h(dansk)o(ere)i(med) e(abonnement)i(til)382 4807 y(analogt)25 b(modem)e(og)h(kun)f(ca.)g (400.000)i(med)e(ISDN)f(og)h(70.000)i(med)e(ADSL)d(\(sv)n(arende)26 b(til)382 4920 y(andelene)g(86\045,)d(12\045)g(og)h(2\045\).)f (Alts\345)g(er)h(der)g(grundlag)h(for)f(en)g(forbedring.)523 5032 y(Det)18 b(kan)g(virk)o(e)h(m\346rk)o(eligt)g(at)f(ISDN-linjen)h (er)f(nogenlunde)j(lige)e(s\345)f(hurtig)h(som)f(ADSL-)382 5145 y(forbindelsen,)31 b(men)d(det)h(kan)g(sk)o(yldes)g(at)f(der)h(o)o (v)o(er)f(ISDN-forbindelsen)j(allerede)f(bruges)382 5258 y(k)o(omprimering,)c(se)d(afsnit)i(3.1.3.)1831 5652 y(12)p eop %%Page: 13 15 13 14 bop 1412 228 a FI(Kapitel)25 b(3:)e(Beho)o(vsanalyse)p 382 266 2989 4 v 382 548 a Fw(3.1.3)99 b(K)n(ompr)n(ession)24 b(af)h(f)n(orbindelser)382 722 y FJ(Noget,)30 b(der)h(kan)g(under)n (gra)n(v)o(e)i(ideen)f(i)e(at)g(k)o(omprimere)i(HTML-\002lerne,)d(er)l (,)h(hvis)h(forbin-)382 835 y(delserne)26 b(allerede)f(bli)n(v)o(er)f (k)o(omprimeret.)523 948 y(P\345)h(st\370rre)j(forbindelser)h(\226)d (f.eks.)g(o)o(v)o(er)g(Atlanterha)n(v)o(et)j(og)e(p\345)f(ruter)h (internetudbydere)382 1061 y(imellem)35 b(\226)f(ben)o(yttes)j(der)e (ingen)g(k)o(ompression.)j(\305rsagen)e(til)e(dette)i(er)e (formodentlig)k(at)382 1174 y(hardw)o(arekra)n(v)o(ene)i(til)c(at)g(k)o (omprimere)i(s\345)e(store)h(m\346ngder)g(data)g(tilstr\346kk)o(eligt)i (hurtigt)382 1287 y(g\370r)24 b(det)g(for)f(dyrt.)523 1400 y(I)k(teknologien)k(for)d(analoge)i(modemer)e(er)f(der)h (imidlertid)i(allerede)f(indbygget)i(k)o(om-)382 1513 y(pression)23 b([3)q(])e(i)g(form)g(af)g(V)-12 b(.42bis)22 b(som)f(ben)o(ytter)i(en)f(v)n(ariant)g(af)f(LZW)f(\(se)h(e)n(vt.)g (afsnit)i(5.2.2\).)382 1625 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b(unders\370gelser)j(har)c(heller)h (ikk)o(e)g(vist,)g(at)f(ADSL-opk)o(oblinger)i(ben)o(ytter)g(hardw)o(a-) 382 2642 y(rek)o(ompression.)39 b(Der)d(er)g(dog)h(foresl\345et)h(en)f (standard)h([15)q(],)e(som)f(medf\370rer)j(at)e(ADSL-)382 2755 y(forbindelser)e(kan)e(ben)o(ytte)h(LZ-Stac.)c(En)i(del)g(routere) i(og)e(lignende)i(udstyr)g(kan)e(ben)o(ytte)382 2868 y(denne)25 b(standard)g(og)f(at)f(stadigt)j(mere)d(hardw)o(are)i (underst\370tter)i(det.)523 2980 y(Som)d(n\346vnt)i(er)f(LZ-Stac)f(kun) h(en)h FD(for)m(esl\345et)i FJ(standard.)f(Det)e(betyder)i(ogs\345,)e (at)g(der)h(v)o(ed)382 3093 y(oprettelse)37 b(af)d(opkaldsforbindels)q (er)40 b(forhandles,)d(om)d(der)h(skal)g(ben)o(yttes)h(k)o(ompression.) 382 3206 y(Det)25 b(vil)h(sige,)h(at)e(det)i(kr\346v)o(er)l(,)f(at)g (internetudbyderne)31 b(underst\370tter)e(og)d(ben)o(ytter)i(LZ-Stac,) 382 3319 y(for)c(at)f(man)g(kan)h(bruge)h(det.)382 3612 y FB(3.2)119 b(Udbyder)n(ne)382 3819 y FJ(Mens)21 b(besparelser)i 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3290 y(8)24 b(Mbit)275 b(180.000)p 1393 3347 967 8 v 1028 3525 a FD(T)-8 b(abel)24 b(3.4:)31 b(Priseksempel)25 b(fr)o(a)f(Cyber)m(city)g(Erhverv)523 3736 y FJ(Med)e(hensyn)i(til)f (kra)n(v)g(til)g(k)o(ompressionsmetoden)k(har)c(unders\370gelserne)k (af)c(datasam-)382 3849 y(mens\346tningen)35 b(vist)f(at)f(andelen)i (af)e(dynamisk)o(e)i(sider)g(i)d(forhold)j(til)e(statisk)o(e)i(er)e (s\345)g(stor)382 3962 y(at)d(der)h(er)f(beho)o(v)h(for)f(en)h(metode)g (der)f(ogs\345)i(kan)e(bruges)i(p\345)e(dynamisk)o(e)j(sider)e(\226)f (for)h(ud-)382 4075 y(byderne)e(kan)e(dette)h(betyde)g(st\370rre)h(kra) n(v)e(til)g(serv)o(ernes)i(bere)o(gningskraft)j(fordi)27 b(denne)i(m\345)382 4188 y(fore)o(g\345)e(l\370bende,)g(statisk)o(e)h (sider)f(ville)g(bare)f(kunne)i(k)o(omprimeres)g(en)e(gang)g(for)g (alle,)g(men)382 4301 y(n\345r)32 b(de)g(i)f(forv)o(ejen)j(har)e(in)l (v)o(esteret)j(en)d(del)g(i)f(den)i(for)f(at)f(kunne)j(oms\346tte)e(de) g(dynamisk)o(e)382 4414 y(sider)24 b(til)g(HTML,)d(er)i(det)h(muligvis) h(relati)n(vt)g(billigt)g(at)e(foretage)j(den)e(forn\370dne)i (udvidelse.)523 4527 y(Desuden)f(er)f(en)g(stor)h(del)f(af)g (websiderne)i(ret)f(sm\345,)e(dvs.)h(under)i(10)e(kb,)g(s\345)g (medmindre)382 4640 y(metoden)32 b(ogs\345)f(er)f(ef)n(fekti)n(v)i (p\345)f(sm\345)f(\002ler)l(,)g(kan)h(en)g(del)g(af)f(ge)n(vinsten)j (forsvinde)g(\(mindre)382 4753 y(\002ler)24 b(fylder)h(dog)g(ikk)o(e)g (s\345)f(me)o(get)h(s\345)f(de)g(udg\370r)i(forholdsm\346ssigt)h (mindre)e(af)f(den)h(samlede)382 4865 y(datam\346ngde\).)523 4978 y(Kra)n(v)o(ene)f(til)g(en)g(k)o(ompressionsalgoritme)29 b(er)23 b(alts\345)i(at)e(den)518 5166 y Fs(\017)46 b FJ(er)24 b(ef)n(fekti)n(v)g(p\345)g(HTML-sider)518 5354 y Fs(\017)46 b FJ(kan)24 b(bruges)h(i)e(forbindelse)k(med)c(dynamisk)o (e)j(sider)1831 5652 y(15)p eop %%Page: 16 18 16 17 bop 1412 228 a FI(Kapitel)25 b(3:)e(Beho)o(vsanalyse)p 382 266 2989 4 v 518 548 a Fs(\017)46 b FJ(ikk)o(e)26 b(er)f(for)g(bere)o(gningskr\346v)o(ende,)30 b(dvs.)25 b(er)g(hurtig)i(til)e(at)g(k)o(omprimere)i(og)e(dek)o(om-)609 661 y(primere)518 848 y Fs(\017)46 b FJ(er)24 b(god)g(til)f(sm\345)g (s\345v)o(el)i(som)e(store)h(\002ler)382 1036 y(Nogle)f(af)f(disse)i (kra)n(v)f(kan)g(v\346re)g(i)f(k)o(on\003ikt)i(med)e(hinanden)j(s\345)e (en)f(gi)n(v)o(en)i(algoritmes)g(e)o(gen-)382 1149 y(skaber)h(m\345)e (afh\346nge)h(af)g(en)f(afv)o(ejning.)523 1262 y(N\345r)g(potentialet)j (for)e(en)f(k)o(ompressionl\370sning)29 b(og)23 b(nogle)i(kra)n(v)f (til)f(den)h(s\345ledes)h(er)e(ble-)382 1375 y(v)o(et)h(f)o (astsl\345et,)i(kan)f(vi)g(g\345)f(o)o(v)o(er)g(til)h(at)f(de\002nere)h (selv)o(e)g(k)o(ompressionsbe)o(grebe)q(t,)k(f\370rst)c(fra)g(en)382 1488 y(teoretisk)h(synspunkt)g(i)d(form)h(af)f(be)o(grebet)i FD(informationsteori)p FJ(.)1831 5652 y(16)p eop %%Page: 17 19 17 18 bop 382 1171 a FC(Kapitel)43 b(4)382 1586 y FK(Inf)-5 b(ormationsteori)382 2031 y FJ(Informationsindholde)q(t)43 b(er)38 b(som)g(n\346vnt)g(i)g(indledningen)j(ikk)o(e)e(n\370dv)o (endigvis)j(lig)c(med)382 2144 y(st\370rrelsen)c(af)e(data.)g(Hv)n (ordan)h(\002nder)f(man)f(da)h(ud)f(af)h(hv)n(or)g(me)o(get)g (information)i(der)e(er)f(i)382 2257 y(en)23 b(gi)n(v)o(en)i(m\346ngde) e(data?)523 2369 y(En)32 b(m\345de)h(at)g(gribe)g(problemet)i(an)e (p\345)g(er)f(at)h(stille)h(en)f(r\346kk)o(e)g(ja/nej-sp\370r)n (gsm\345l)38 b(om)382 2482 y(dataene)24 b(\226)e(er)g(det)h(n\346ste)g (te)o(gn)f(et)h(bogsta)n(v?)i(Er)c(det)i(et)f(stort)h(bogsta)n(v?)i(Er) c(det)i(et)f(`a'?)h(Er)f(det)382 2595 y(et)h(`b'?)523 2708 y(Et)c(ja)h(eller)h(et)f(nej)g(kan)h(opf)o(attes)h(som)e(enten)h (et)f(0)f(eller)i(et)f(1)g(s\345)g(r\346kk)o(en)h(af)f(sv)n(ar)g(bli)n (v)o(er)h(til)382 2821 y(en)h(bin\346r)h(streng.)g(Hvis)f(vi)h(opf)o (atter)h(dataene)g(som)e(adskilte)i(te)o(gn,)f(kan)g(m\345let)f(for)h (informa-)382 2934 y(tion)29 b(v\346re)g(det)g(gennemsnitlige)j(antal)e (af)e(sp\370r)n(gsm\345l,)j(sv)n(arende)f(til)f(den)g(gennemsnitlige) 382 3047 y(l\346ngde)22 b(af)e(de)h(bin\346re)h(strenge,)g(der)f(er)g (n\370dv)o(endige)j(for)d(at)g(kunne)h(identi\002cere)h(hv)o(ert)f(te)o (gn.)523 3160 y(Antallet)37 b(af)f(n\370dv)o(endige)i(sp\370r)n (gsm\345l)h(afh\346nger)e(imidlertid)g(af)f(sandsynlighederne)382 3273 y(for)g(de)g(enk)o(elte)h(udf)o(ald;)h(hvis)e(et)g(gi)n(v)o(ent)g (udf)o(ald)h(v)n(ar)f(me)o(get)g(sandsynligt)j(kunne)e(det)f(jo)382 3386 y(f.eks.)30 b(godt)g(betale)h(sig)f(at)f(starte)i(med)e(at)h (sp\370r)n(ge)h(direkte)h(efter)e(netop)h(det)f(udf)o(ald,)h(mens)382 3499 y(hvis)26 b(modsat)f(alle)h(udf)o(ald)g(v)n(ar)f(omtrent)h(lige)f (sandsynlige,)j(kunne)f(det)e(bedst)h(betale)g(sig)f(at)382 3611 y(sp\370r)n(ge)g(om)e(det)h(k)o(onkrete)i(udf)o(ald)f(v)n(ar)f(et) g(fra)f(den)h(ene)g(halvdel)i(af)d(udf)o(aldene)k(\226)c(s\345)g(\002k) g(man)382 3724 y(hurtigst)i(muligt)g(indkredset)h(det.)382 4017 y FB(4.1)119 b(Entr)n(opi)382 4224 y FJ(Antallet)32 b(af)e(n\370dv)o(endige)k(sp\370r)n(gsm\345l)f(til)d(et)h(me)o(get)f (sandsynligt)k(udf)o(ald)e(er)f(alts\345)g(mindre)382 4337 y(end)23 b(for)g(et)f(med)g(en)h(lille)g(sandsynlighed,)k(hvilk)o (et)d(kan)f(opf)o(attes)i(som)d(at)h(informationsind-)382 4450 y(holdet)31 b(for)f(det)f(f\370rste)i(udf)o(ald)g(er)f(mindre)g (end)g(for)f(det)h(andet.)h(Dette)e(forhold)j(kan)e(opn\345s)382 4563 y(matematisk)f(v)o(ed)e(at)h(de\002nere)g(informationsindholde)q (t)33 b(for)27 b(et)h(gi)n(v)o(ent)g(udf)o(ald)h(som)e([17)q(,)g(s.)382 4676 y(14])1411 4880 y Fu(i)p Fr(\()p Fu(x)p Fr(\))f(=)f Fs(\000)15 b Fr(log)1890 4902 y Ft(2)1944 4880 y Fu(P)e Fr(\()p Fu(X)33 b Fr(=)25 b Fu(x)p Fr(\))382 5084 y FJ(hv)n(or)32 b Fu(x)e FJ(er)h(et)g(udf)o(ald)i(for)e(en)g(diskret)i(stokastisk)h(v)n (ariabel)f Fu(X)38 b FJ(og)31 b Fu(P)13 b Fr(\()p Fu(X)47 b Fr(=)39 b Fu(x)p Fr(\))31 b FJ(sandsyn-)382 5197 y(ligheden)39 b(for)e(at)g(udf)o(aldet)j(optr\346der)e(\(vi)f(ben)o(ytter)i(herefter) g(en)e(k)o(ortere)i(notation)g(hv)n(or)382 5310 y Fu(p)p Fr(\()p Fu(x)p Fr(\))26 b(=)f Fu(P)13 b Fr(\()p Fu(X)33 b Fr(=)25 b Fu(x)p Fr(\))p FJ(\).)c(Her)g(er)g(ben)o(yttet)j (totalslogaritmen)h(hv)n(ad)e(der)f(gi)n(v)o(er)g(resultatet)i(i)d (bit,)1831 5652 y(17)p eop %%Page: 18 20 18 19 bop 1366 228 a FI(Kapitel)25 b(4:)e(Informationsteori)p 382 266 2989 4 v 382 548 a FJ(andre)h(logaritmer)g(gi)n(v)o(er)f(en)g (anden)h(enhed)h(der)e(dog)g(kun)h(afviger)g(fra)f(bit-enheden)j(med)d (en)382 661 y(k)o(onstant)j(f)o(aktor)f([4,)e(s.)g(14].)523 774 y(F)o(\370r)18 b(vi)h(kan)h(forts\346tte,)g(skal)g(vi)f(ha)n(v)o(e) h(de\002nitionen)i(af)d(et)g FD(alfabet)k FJ(p\345)c(plads.)h(Et)e(alf) o(abet)j Fq(A)382 887 y FJ(er)f(m\346ngden)h(af)f(forsk)o(ellige)j (symboler)f(som)d(en)i(algoritme)g(kan)g(\002nde)f(i)g(en)g(gi)n(v)o (en)h(m\346ngde)382 1000 y(data;)28 b(f.eks.)f(kan)h(\204abccba\223)i (repr\346senteres)g(vha.)d(alf)o(abetet)j Fq(A)58 b Fr(=)32 b Fs(f)p Fu(a;)15 b(b;)g(c)p Fs(g)p FJ(,)28 b(men)f(det)g(kan)382 1112 y(ogs\345)d(repr\346senteres)j(vha.)d Fq(B)44 b Fr(=)25 b Fs(f)p Fu(abc;)15 b(cba)p Fs(g)p FJ(.)523 1225 y(F)o(or)28 b(en)g(gi)n(v)o(en)h(diskret)h(stokastisk)i(v)n(ariabel)e Fu(X)35 b FJ(hvis)30 b(udf)o(aldsrum)g(er)f(alf)o(abetet)i Fq(A)19 b FJ(,)34 b(og)382 1338 y(hvis)26 b(udf)o(ald)g(er)f(bestemt)h (af)e(sandsynlighedsfo)q(rde)q(lin)q(gs)q(fun)q(kt)q(ion)q(en)31 b Fu(p)p Fr(\()p Fu(x)p Fr(\))p FJ(,)24 b(de\002nerer)i(man)382 1451 y(s\345)34 b FD(entr)l(opien)i Fu(H)7 b Fr(\()p Fu(X)g Fr(\))34 b FJ(som)f(den)i(forv)o(entede)h(middelv\346rdi)f(af)f (informationsindhold)q(ene)382 1564 y(for)24 b(alle)g(udf)o(aldene)i ([4)q(,)c(s.)h(13]:)1021 1881 y Fu(H)7 b Fr(\()p Fu(X)g Fr(\))26 b(=)1380 1795 y Fp(X)1378 1992 y Fo(x)p Fn(2)p Fm(A)1528 1881 y Fu(p)p Fr(\()p Fu(x)p Fr(\))p Fu(i)p Fr(\()p Fu(x)p Fr(\))h(=)e Fs(\000)2059 1795 y Fp(X)2058 1992 y Fo(x)p Fn(2)p Fm(A)2208 1881 y Fu(p)p Fr(\()p Fu(x)p Fr(\))15 b(log)2509 1903 y Ft(2)2563 1881 y Fu(p)p Fr(\()p Fu(x)p Fr(\))523 2171 y FJ(T)-7 b(ag)19 b(som)g(et)g(eksempel)i (den)f(stokastisk)o(e)i(v)n(ariabel)f(i)e(tabel)i(4.1)e(som)g(bygger)i (p\345)e(te)o(gnf\370l-)382 2284 y(gen)g(\204aaabbcbcbcababaa)q(\223)24 b(med)18 b(alf)o(abetet)j Fs(f)p Fu(a;)15 b(b;)g(c)p Fs(g)p FJ(.)20 b(Ud)d(fra)i(sandsynlighedsfor)q(del)q(ing)q(en)382 2397 y(kan)24 b(entropien)i(bere)o(gnes)f(til)842 2601 y Fu(H)32 b Fr(=)25 b Fs(\000)1142 2574 y Fl(7)p 1127 2586 61 3 v 1127 2627 a(16)1218 2601 y Fs(\001)20 b Fr(log)1381 2623 y Ft(2)1460 2574 y Fl(7)p 1445 2586 V 1445 2627 a(16)1536 2601 y Fs(\000)1652 2574 y Fl(6)p 1637 2586 V 1637 2627 a(16)1728 2601 y Fs(\001)h Fr(log)1891 2623 y Ft(2)1971 2574 y Fl(6)p 1956 2586 V 1956 2627 a(16)2047 2601 y Fs(\000)2163 2574 y Fl(3)p 2148 2586 V 2148 2627 a(16)2239 2601 y Fs(\001)f Fr(log)2402 2623 y Ft(2)2481 2574 y Fl(3)p 2466 2586 V 2466 2627 a(16)2562 2601 y Fr(=)25 b(1)p Fu(;)p Fr(5052)p 1472 2833 810 8 v 1564 2937 a Fu(X)171 b FJ(a)138 b(b)g(c)p 1472 2991 810 5 v 1521 3096 a Fu(p)p Fr(\()p Fu(x)p Fr(\))1815 3069 y Fl(7)p 1799 3081 61 3 v 1799 3122 a(16)1995 3069 y(6)p 1980 3081 V 1980 3122 a(16)2176 3069 y(3)p 2160 3081 V 2160 3122 a(16)p 1472 3153 810 8 v 933 3338 a FD(T)-8 b(abel)24 b(4.1:)31 b(F)-5 b(r)m(ekvensfor)m(deling)27 b(med)c(alfabetet)j Fs(f)p Fu(a;)15 b(b;)g(c)p Fs(g)523 3539 y FJ(Hvis)j(man)g(betragter)i(te)o(gnf\370lgen,)h(ses)d(det)g(at)g (vi)g(ogs\345)h(kan)g(bruge)g(alf)o(abetet)h Fs(f)p Fu(aa;)15 b(ab;)g(bc)p Fs(g)382 3652 y FJ(da)24 b(a,)f(b)h(og)g(c)f(kun)i (optr\346der)g(i)e(denne)j(r\346kk)o(ef\370lge.)g(Hvis)d(man)h(g\370r)g (det,)g(bli)n(v)o(er)h(entropien)h(i)382 3765 y(stedet)933 3969 y Fu(H)32 b Fr(=)25 b Fs(\000)1218 3942 y Fl(2)p 1218 3954 31 3 v 1218 3995 a(8)1279 3969 y Fs(\001)20 b Fr(log)1442 3991 y Ft(2)1506 3942 y Fl(2)p 1506 3954 V 1506 3995 a(8)1567 3969 y Fs(\000)1668 3942 y Fl(3)p 1668 3954 V 1668 3995 a(8)1728 3969 y Fs(\001)h Fr(log)1891 3991 y Ft(2)1956 3942 y Fl(3)p 1956 3954 V 1956 3995 a(8)2016 3969 y Fs(\000)2117 3942 y Fl(3)p 2117 3954 V 2117 3995 a(8)2178 3969 y Fs(\001)f Fr(log)2341 3991 y Ft(2)2405 3942 y Fl(3)p 2405 3954 V 2405 3995 a(8)2471 3969 y Fr(=)25 b(1)p Fu(;)p Fr(5613)523 4173 y FJ(Entropien)h (afh\346nger)g(alts\345)f(hv)n(ordan)i(man)d(v\346lger)h(sit)f(alf)o (abet.)i(V)-10 b(ed)24 b(at)g(v\346lge)h(et)f(med)382 4286 y(blokk)o(e)d(af)e(to)g(te)o(gn,)g(har)h(vi)f(n\346sten)h(halv)o (eret)g(entropien)i(\226)d(1,505)h(bit)f(pr)-5 b(.)19 b(symbol)h(mod)f(1,561)382 4399 y(bit)24 b(pr)-5 b(.)23 b(to)g(datate)o(gn)j(sv)n(arende)f(til)f(0,7807)g(bit)g(pr)-5 b(.)23 b(datate)o(gn.)382 4692 y FB(4.2)119 b(Egenskaber)30 b(v)o(ed)g(entr)n(opi)382 4899 y FJ(Man)19 b(kan)h(be)n(vise)g(nogle)g (interessante)j(tr\346k)c(v)o(ed)g Fu(H)7 b Fr(\()p Fu(X)g Fr(\))20 b FJ(\226)f(det)g(er)g(f)o(aktisk)i(disse)f(e)o(genskaber)382 5012 y(der)27 b(g\370r)f(at)h(entropi)h(er)e(et)g(n)o(yttigt)i(be)o (greb)g(at)e(besk\346ftige)j(sig)d(med.)g(S\346tningerne)i(vil)f(ikk)o (e)382 5125 y(bli)n(v)o(e)e(be)n(vist)g(her)l(,)g(da)f(en)g (udt\370mmende)i(be)n(visf\370relse)i(ikk)o(e)d(er)f(rele)n(v)n(ant)i (for)e(projektet)j(som)382 5237 y(helhed.)1831 5652 y(18)p eop %%Page: 19 21 19 20 bop 1366 228 a FI(Kapitel)25 b(4:)e(Informationsteori)p 382 266 2989 4 v 382 548 a Fw(4.2.1)99 b(Optimal)24 b(k)o(odning)382 722 y FJ(N\345r)32 b(man)f(skal)i(v\346lge)g(et)f(alf)o(abet)i(og)e (dets)h(repr\346sentation)i(i)d(form)g(af)g(k)o(odeord,)i(g\346lder)382 835 y(det)24 b(naturligvis)j(om)d(at)g(k)o(odeordene)j(resulterer)g(i)c (den)i(k)o(ortest)h(mulige)f(tekst)g(n\345r)f(de)g(bli)n(v)o(er)382 948 y(sat)h(sammen)h(til)f(den)g(k)o(omprimerede)j(tekst.)e(Der)e(er)h (eksisterer)j(alts\345)e FD(optimale)g FJ(k)o(oder)h(der)382 1061 y(gi)n(v)o(er)22 b(et)f(bedre)i(k)o(ompressionsforhold)k(end)22 b(alle)g(andre)h(k)o(oder)g(p\345)e(en)h(gi)n(v)o(en)g(m\346ngde)g (data.)523 1174 y(Hvis)g Fu(l)743 1188 y Ft(1)782 1174 y Fu(;)15 b(l)849 1188 y Ft(2)904 1174 y Fu(:)g(:)g(:)i(l)1053 1188 y Fo(n)1121 1174 y FJ(er)k(l\346ngderne)j(af)d(de)h(optimale)h(k)o (odeord)h(for)e(en)g(stokastisk)i(v)n(ariabel)382 1287 y Fu(X)42 b FJ(med)35 b(sandsynlighedsford)q(elin)q(ge)q(n)40 b Fu(p)p Fr(\()p Fu(x)p Fr(\))p FJ(,)35 b(og)g Fu(L)f FJ(er)h(den)h(forv)o(entede)i(l\346ngde)d(af)g(den)382 1400 y(optimale)25 b(k)o(ode)f(\()p Fu(L)i Fr(=)1135 1331 y Fp(P)1246 1400 y Fu(p)p Fr(\()p Fu(x)1379 1414 y Fo(i)1407 1400 y Fr(\))p Fu(l)1469 1414 y Fo(i)1498 1400 y FJ(\),)c(g\346lder)j(s\345)e([4)q(,)f(s.)h(86\22688])1410 1572 y Fu(H)7 b Fr(\()p Fu(X)g Fr(\))26 b Fs(\024)f Fu(L)g Fs(\024)g Fu(H)7 b Fr(\()p Fu(X)g Fr(\))21 b(+)f(1)382 1744 y FJ(Det)i(vil)h(sige)g(at)f(den)h(mindste)h(m\346ngde)f(data)g (man)f(kan)h(bruge)h(til)f(at)f(repr\346sentere)j(et)e(te)o(gn,)382 1857 y(ligger)g(inden)g(for)f(\351n)g(bit)g(af)f(entropien)k(af)c (dataene.)i(V)-5 b(i)21 b(kan)h(presse)h(dataene)h(ned)e(til)g Fu(H)7 b Fr(\()p Fu(X)g Fr(\))p FJ(,)382 1970 y(men)23 b(s\345)h(heller)g(ikk)o(e)h(l\346ngere.)523 2083 y(At)c(det)i (optimale)h(ligger)f(inden)h(for)e(\351n)h(bit)f(og)g(ikk)o(e)i(er)e (mindre,)h(h\346nger)g(sammen)f(med)382 2196 y(at)i(der)h(er)g(et)g (vist)g(spild)h(hvis)f(entropien)i(ikk)o(e)f(gi)n(v)o(er)f(et)f(helt)i (tal)f(\226)f(vi)h(kan)g(ikk)o(e)g(sende)h(halv)o(e)382 2309 y(bit.)f(Dette)g(problem)h(kan)g(formindsk)o(es)h(v)o(ed)e(at)g(k) o(ode)h(st\370rre)g(blokk)o(e)h(af)e(gangen)h(s\345)f(spildet)382 2421 y(bli)n(v)o(er)f(spredt)h(ud)f(p\345)f(\003ere)g(te)o(gn)h(og)g (dermed)g(samlet)g(bli)n(v)o(er)h(mindre.)382 2665 y Fw(4.2.2)99 b(Maksimal)24 b(entr)n(opi)i(v)o(ed)f(ligelig)f(f)n (ordeling)382 2840 y FJ(Hvis)g Fu(n)e FJ(er)h(antallet)j(af)e(udf)o (ald)h(i)e(fordelingen)k(for)d Fu(X)7 b FJ(,)23 b(opn\345s)i(den)f (maksimale)h(entropi)g(hvis)382 2953 y(sandsynlighederne)36 b(for)30 b(udf)o(aldene)i(er)e(ens)g(\()p Fu(p)p Fr(\()p Fu(x)p Fr(\))38 b(=)2216 2925 y Fl(1)p 2212 2937 39 3 v 2212 2979 a Fk(n)2261 2953 y FJ(\),)29 b(og)g(har)i(v\346rdien)g Fr(log)3047 2974 y Ft(2)3102 2953 y Fu(n)d FJ([4)q(,)h(s.)382 3065 y(27].)523 3178 y(Hvis)20 b(f.eks.)g Fu(X)26 b FJ(kan)20 b(antage)i(256)e(v\346rdier)h(med)e(lige)h(stor)h(sandsynlighed,)j(er) 19 b(entropien)382 3291 y Fu(H)7 b Fr(\()p Fu(X)g Fr(\))52 b(=)e(log)907 3313 y Ft(2)947 3291 y Fr(\(256\))i(=)e(8)24 b FJ(bit)q(.)36 b(Hvis)h(der)g(er)g(forsk)o(el)i(p\345)e (sandsynlighedern)q(e,)42 b(bli)n(v)o(er)382 3404 y(entropien)26 b(mindre)e(end)g(8)f(bit.)523 3517 y(Denne)d(e)o(genskab)h (fort\346ller)g(noget)g(om)d(hv)n(orfor)k(almindelige)f(data)f(normalt) h(kan)f(k)o(om-)382 3630 y(primeres.)29 b(Hvis)f(en)g(te)o(gnf\370lge)i (er)e(genereret)j(helt)d(tilf\346ldigt,)i(vil)e(de)g(forsk)o(ellige)j (v\346rdier)382 3743 y(naturligvis)f(optr\346de)d(med)f(nogenlunde)k (samme)d(sandsynlighed)k(hvis)c(man)f(betragter)j(en)382 3856 y(tilstr\346kk)o(eligt)c(stor)d(datam\346ngde)h(\226)e(det)h(vil)g (sige)g(at)f(entropien)j(for)e(s\345dan)g(en)g(te)o(gnf\370lge)i(vil) 382 3969 y(ligge)e(lige)g(omkring)h(en)e(almindelig)i (repr\346sentation)i(af)c(te)o(gnene)i(hv)n(or)f(man)f(bruger)i(et)e(f) o(ast)382 4082 y(antal)j(bit,)g(alts\345)g(kan)g(disse)h(ikk)o(e)f(k)o (omprimeres.)523 4195 y(F)o(or)29 b(data)h(der)g(ikk)o(e)g(er)g (genereret)i(helt)e(tilf\346ldigt,)h(vil)f(der)g(derimod)g(som)g(re)o (gel)g(v\346re)382 4307 y(en)d(struktur)i(der)e(g\370r)g(at)g(nogle)h (ting)f(g\345r)g(igen)h(mange)f(gange.)h(F)-7 b(.eks.)26 b(optr\346der)i(`e')f(me)o(get)382 4420 y(hyppigere)f(end)e(`z')f(i)g (en)h(almindelig)i(dansk)e(tekst,)h(og)e(dermed)i(bli)n(v)o(er)f (entropien)i(mindre.)523 4533 y(Det)33 b(kan)i(virk)o(e)f(m\346rk)o (eligt)h(at)f(helt)g(tilf\346ldige)i(data)e(indeholder)j(mere)c (information)382 4646 y(end)e(omhyggeligt)j(udformede,)e(mennesk)o (eskabte)j(data,)d(men)e(den)i(mennesk)o(elige)i(bear)n(-)382 4759 y(bejdningsproces)27 b(er)22 b(jo)g(netop)i(g\345et)f(ud)f(p\345)g (at)g(sortere)i(og)f(ordne)g(dataene.)h(En)d(st\370rre)j(orden)382 4872 y(gi)n(v)o(er)g(f\346rre)f(muligheder)l(,)j(og)e(g\370r)g(det)g (muligt)g(at)f(forudsige)j(data.)382 5116 y Fw(4.2.3)99 b(Afh\346ngigheder)26 b(r)n(educer)n(er)i(entr)n(opi)382 5290 y FJ(I)21 b(almindelig)i(tekst)f(optr\346der)h(te)o(gnene)g(med)e (en)g(vis)h(indbyrdes)i(afh\346ngighed.)g(Hvis)d(f.eks.)382 5403 y(bogsta)n(v)o(erne)35 b(\204b)p Fu(x)p FJ(ld\223)d(st\345r)g(i)f (en)h(dansk)g(tekst,)h(er)e(der)h(en)f(me)o(get)h(stor)g(sandsynlighed) k(for)1831 5652 y(19)p eop %%Page: 20 22 20 21 bop 1366 228 a FI(Kapitel)25 b(4:)e(Informationsteori)p 382 266 2989 4 v 382 548 a FJ(at)29 b Fu(x)f FJ(enten)i(er)f(et)g(`o')h (eller)f(et)g(`y'.)h(Det)e(viser)i(sig)g(at)f(indbyrdes)i (afh\346ngigheder)i(mellem)382 661 y(te)o(gnene)27 b(for\345rsager)h (at)e(entropien)i(reduceres.)g(F)o(\370rst)d(er)h(der)g(dog)g(brug)h (for)f(at)f(f\345)h(de\002neret)382 774 y(f\346lles)e(entropi)h(og)f (betinget)h(entropi.)523 887 y(Den)c FD(f\346lles)g(entr)l(opi)i Fu(H)7 b Fr(\()p Fu(X)r(;)15 b(Y)21 b Fr(\))g FJ(for)g(to)g(diskrete)i (stokastisk)o(e)h(v)n(ariable)f(med)e(den)h(f\346lles)382 1000 y(sandsynlighedsford)q(el)q(ing)29 b Fu(p)p Fr(\()p Fu(X)r(;)15 b(Y)21 b Fr(\))i FJ(er)h(de\002neret)h(som)e([4)q(,)f(s.)h (15])1062 1217 y Fu(H)7 b Fr(\()p Fu(X)r(;)15 b(Y)21 b Fr(\))26 b(=)f Fs(\000)1614 1131 y Fp(X)1667 1326 y Fo(i)1760 1131 y Fp(X)1810 1326 y Fo(j)1907 1217 y Fu(p)p Fr(\()p Fu(x)2040 1231 y Fo(i)2068 1217 y Fu(;)15 b(y)2153 1231 y Fo(j)2189 1217 y Fr(\))g(log)i Fu(p)p Fr(\()p Fu(x)2505 1231 y Fo(i)2534 1217 y Fu(;)e(y)2619 1231 y Fo(j)2655 1217 y Fr(\))382 1516 y FJ(mens)24 b(den)g FD(beting)o(ede)i(entr)l(opi)f Fu(H)7 b Fr(\()p Fu(X)g Fs(j)p Fu(Y)21 b Fr(\))i FJ(er)h(de\002neret)g(som)976 1734 y Fu(H)7 b Fr(\()p Fu(X)g Fs(j)p Fu(Y)21 b Fr(\))26 b(=)1432 1648 y Fp(X)1481 1843 y Fo(j)1578 1734 y Fu(p)p Fr(\()p Fu(y)1704 1748 y Fo(j)1740 1734 y Fr(\))p Fu(H)7 b Fr(\()p Fu(X)g Fs(j)p Fu(Y)47 b Fr(=)25 b Fu(y)2241 1748 y Fo(j)2277 1734 y Fr(\))1336 1994 y(=)g Fs(\000)1518 1907 y Fp(X)1567 2103 y Fo(j)1664 1994 y Fu(p)p Fr(\()p Fu(y)1790 2008 y Fo(j)1826 1994 y Fr(\))1876 1907 y Fp(X)1930 2103 y Fo(i)2023 1994 y Fu(p)p Fr(\()p Fu(x)2156 2008 y Fo(i)2184 1994 y Fs(j)p Fu(y)2254 2008 y Fo(j)2291 1994 y Fr(\))15 b(log)i Fu(p)p Fr(\()p Fu(x)2607 2008 y Fo(i)2635 1994 y Fs(j)p Fu(y)2705 2008 y Fo(j)2741 1994 y Fr(\))1336 2254 y(=)25 b Fs(\000)1518 2167 y Fp(X)1571 2363 y Fo(i)1664 2167 y Fp(X)1713 2363 y Fo(j)1810 2254 y Fu(p)p Fr(\()p Fu(x)1943 2268 y Fo(i)1972 2254 y Fu(;)15 b(y)2057 2268 y Fo(j)2093 2254 y Fr(\))g(log)i Fu(p)p Fr(\()p Fu(x)2409 2268 y Fo(i)2437 2254 y Fs(j)p Fu(y)2507 2268 y Fo(j)2544 2254 y Fr(\))382 2546 y FJ(hv)n(or)26 b(vi)e(har)h(ben)o(yttet)i(de\002nitionen)g(for)e(entropi)i(og)e(skre)n (v)o(et)g(lidt)h(om.)e(Den)g(f\346lles)h(entropi)382 2659 y(kan)f(vha.)g(en)f(k\346dere)o(gel)i(udvides)h(til)d(at)h(opf)o (atte)h(\003ere)e(v)n(ariable)i(med)f(f\346lles)g(fordeling.)523 2772 y(Man)34 b(kan)g(da)f(be)n(vise)i([4)q(,)e(s.)g(27\22628])i(at)f (for)g(to)f(afh\346ngige)j(stokastisk)o(e)h(v)n(ariable)e Fu(X)382 2885 y FJ(og)24 b Fu(Y)43 b FJ(med)23 b(en)h(f\346lles)g (sandsynlighedsford)q(el)q(ing)30 b Fu(p)p Fr(\()p Fu(X)r(;)15 b(Y)21 b Fr(\))p FJ(,)h(vil)i(entropien)j(for)d Fu(X)30 b FJ(gi)n(v)o(et)24 b(at)382 2998 y(udf)o(aldet)i(af)d Fu(Y)43 b FJ(er)23 b(k)o(endt,)i(v\346re)e(mindre)h(end)g(entropien)i (for)e(blot)g Fu(X)7 b FJ(:)1530 3202 y Fu(H)g Fr(\()p Fu(X)g Fs(j)p Fu(Y)21 b Fr(\))26 b Fu(<)f(H)7 b Fr(\()p Fu(X)g Fr(\))523 3406 y FJ(Det)23 b(kan)h(bl.a.)g(be)n(vises)h(at)e(ha) n(v)o(e)i(den)f(f\370lge)g(at)g(entropien)i(for)e(en)f(blok)i(af)e(te)o (gn)h(altid)h(vil)382 3519 y(v\346re)e(mindre)i(end)f(\(eller)g(e)n (vt.)f(lig)h(med\))g(de)f(sammenlagte)j(entropier)g(for)d(de)h(enk)o (elte)h(te)o(gn)808 3723 y Fu(H)7 b Fr(\()p Fu(X)1001 3737 y Ft(1)1041 3723 y Fu(;)15 b(X)1156 3737 y Ft(2)1196 3723 y Fu(;)g(:)g(:)g(:)32 b(;)15 b(X)1488 3737 y Fo(n)1536 3723 y Fr(\))25 b Fs(\024)g Fu(H)7 b Fr(\()p Fu(X)1885 3737 y Ft(1)1925 3723 y Fr(\))21 b(+)f Fu(H)7 b Fr(\()p Fu(X)2265 3737 y Ft(2)2305 3723 y Fr(\))20 b(+)g Fu(:)15 b(:)g(:)22 b Fr(+)e Fu(H)7 b Fr(\()p Fu(X)2862 3737 y Fo(n)2909 3723 y Fr(\))382 3927 y FJ(Eksemplet)29 b(fra)f(afsnit)h(4.1) f(hv)n(or)h(entropien)h(ble)n(v)f(halv)o(eret)g(v)o(ed)g(at)e(v\346lge) i(et)f(alf)o(abet)h(med)382 4040 y(blokk)o(e)c(af)f(to)f(te)o(gn,)h (illustrerer)i(dette.)523 4153 y(Ud)k(fra)g(denne)i(e)o(genskab)h (f\345s)d(yderligere)j(en)e(be)o(grundelse)i(for)e(at)f(f.eks.)h (almindelig)382 4266 y(tekst)h(kan)g(k)o(omprimeres.)h(Den)e(struktur)l (,)i(der)f(er)f(i)g(mennesk)o(eskabte)k(data,)d(g\370r)g(at)f(sand-)382 4379 y(synligheden)f(for)c(at)g(et)g(te)o(gn)h(optr\346der)l(,)g (afh\346nger)h(me)o(get)e(af)g(k)o(onteksten.)k(Denne)c(afh\346n-)382 4492 y(gighed)21 b(formindsk)o(er)i(entropien)g(hvis)d(ens)h(model)f (af)g(dataene)i(er)d(i)h(stand)h(til)f(at)g(tage)g(hensyn)382 4605 y(til)j(den,)h(f.eks.)g(v)o(ed)f(at)h(arbejde)h(p\345)f(blokk)o(e) h(af)e(te)o(gn)h(i)f(stedet)i(for)f(kun)g(enk)o(elte.)382 4897 y FB(4.3)119 b(K)m(omprimering)30 b(og)g(entr)n(opi)382 5104 y FJ(Man)c(kan)h(f)o(aktisk)h(vise)f(at)f(en)g(optimal)h(k)o(ode)g (der)g(ligger)g(inden)h(for)e(gr\346nserne)i Fu(H)7 b Fr(\()p Fu(X)g Fr(\))27 b FJ(og)382 5217 y Fu(H)7 b Fr(\()p Fu(X)g Fr(\))26 b(+)e(1)29 b FJ(er)h(mulig)g(at)f(k)o(onstruere)k (\(endda)e(ret)e(simpelt,)i(en)e(algoritme)i(til)f(at)f(g\370re)i(det) 382 5330 y(pr\346senteres)d(i)d(afnit)h(5.1.2\),)g(men)f(som)g(det)h (ogs\345)h(ses)e(er)h(der)g(forsk)o(ellige)i(m\345der)e(man)f(kan)1831 5652 y(20)p eop %%Page: 21 23 21 22 bop 1366 228 a FI(Kapitel)25 b(4:)e(Informationsteori)p 382 266 2989 4 v 382 548 a FJ(formindsk)o(e)31 b(datam\346ngden)h (yderligere)f(p\345.)e(Alt)g(afh\346ngig)h(af)f(hv)n(ordan)i(man)e (v\346lger)h(sit)382 661 y(alf)o(abet,)25 b(repr\346senteret)h(v)o(ed)e (den)g(stokastisk)o(e)j(v)n(ariabel)e Fu(X)7 b FJ(,)23 b(kan)h Fu(H)7 b Fr(\()p Fu(X)g Fr(\))24 b FJ(nemlig)g(v)n(ariere.)523 774 y(F)o(or)g(at)h(optimere)h(k)o(ompressionsforhold)q(et)k(g\346lder) c(det)f(alts\345)g(om)g(at)f(v\346lge)i(en)e(model)382 887 y(der)e(passer)i(til)e(dataene.)i(Hvis)e(modellen)h(har)g(som)f(en) g(grundl\346ggende)k(antagelse)e(at)e(hv)o(ert)382 1000 y(te)o(gn)27 b(er)f(helt)h(uafh\346ngigt)h(af)e(det)h(fore)o (g\345ende,)i(mister)d(man)g(en)h(mulig)f(ge)n(vinst)i(hvis)f(hv)o(ert) 382 1112 y(te)o(gn)20 b(f)o(aktisk)i(afh\346nger)f(til)f(en)g(vis)g (udstr\346kning)j(af)c(sin)i(for)n(g\346nger)h(i)d(de)h(data)h(man)e (ben)o(ytter)382 1225 y(modellen)25 b(p\345.)523 1338 y(Med)31 b(de)h(o)o(v)o(enn\346vnte)h(e)o(genskaber)h(kan)e(vi)f (allerede)j(se)d(at)g(det)h(kan)g(v\346re)f(en)h(fordel)382 1451 y(at)k(sl\345)h(\003ere)g(te)o(gn)g(sammen)g(fordi)h(man)e(s\345)h (dels)g(kan)g(udn)o(ytte)i(afh\346ngigheder)h(mellem)382 1564 y(te)o(gnene,)28 b(afh\346ngigheder)j(der)c(k)o(ommer)h(fra)f(den) g(underliggende)32 b(datastruktur;)f(dels)c(kan)382 1677 y(reducere)f(det)d(spild)i(der)f(opst\345r)h(i)e(forbindelse)j(med)e (generering)i(af)d(k)o(odeordene.)523 1790 y(F)o(or)k(at)h(f\345)f(en)h (fornemmelse)i(af)e(hv)n(ordan)i(informationsindholde)q(t)j(i)27 b(HTML-\002ler)g(ud-)382 1903 y(m\370nter)d(sig,)g(besk\346ftiger)i(vi) d(os)h(i)f(det)g(f\370lgende)j(lidt)e(med)g(deres)g(struktur)-5 b(.)382 2152 y Fw(4.3.1)99 b(HTML,)25 b(inf)n(ormationsteor)n(etisk)g (set)382 2326 y FJ(HTML)37 b(best\345r)j(af)f(bidder)i(af)e(almindelig) i(tekst)f(omgi)n(v)o(et)g(af)f(opm\346rkninger)l(,)i FD(ta)o(gs)p FJ(,)f(af)382 2439 y(hvilk)o(e)34 b(kun)f(et)f(vist)h (antal)g(er)f(gyldige,)i(f.eks.)e(

)g(eller)h(.)29 b(Simple)j(tags)h(som)382 2552 y(de)27 b(n\346vnte)h(er)f (hyppige)i(og)e(indeholder)j(kun)d(lidt)h(information.)h(Imidlertid)g (kan)f(de)f(\003este)382 2665 y(tags)33 b(ogs\345)f(tage)h(parametre,)g (f.eks.)g(,)j(og)e(da)g(indholdet)j(af)d (parame-)382 2778 y(trene)d(ikk)o(e)h(er)e(be)o(gr\346nset)i(p\345)f (nogen)g(m\345de,)g(kan)g(den)g(form)f(for)h(opm\346rkninger)i(besidde) 382 2891 y(et)23 b(st\370rre)i(informationsindhold.)523 3004 y(T)-7 b(ags)32 b(uden)i(parametre)h(kan)e(alts\345)g(teoretisk)j (k)o(omprimeres)e(rigtigt)h(me)o(get,)d(mens)h(vi)382 3117 y(ikk)o(e)26 b(kan)g(forv)o(ente)h(at)e(kunne)h(k)o(omprimere)h (de)e(andre)i(tags)e(s\345)h(me)o(get)f(medmindre)h(de)g(op-)382 3230 y(tr\346der)e(\003ere)f(gange)i(i)e(HTML-\002len.)523 3343 y(Ud)29 b(o)o(v)o(er)g(opm\346rkningen)j(er)d(der)h(ogs\345)g(den) g(almindelige)i(tekst.)e(K)m(ompressionen)i(af)382 3455 y(denne)26 b(kan)f(v\346re)g(me)o(get)f(ef)n(fekti)n(v)i(fordi)g 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y(Huf)n(fman-k)o(odning.)43 b(Denne)e(e)o(genskab) h(v)o(ed)f(Huf)n(fman-k)o(odning)j(har)c(gjort)h(den)g(me)o(get)382 1000 y(ben)o(yttet)32 b(i)e(k)o(ombination)k(med)c(andre)i(metoder)-5 b(.)31 b(Eksempelvis)i(bruger)f FA(gzip)d FJ(og)i FA(bzip2)382 1112 y FJ(Huf)n(fman-k)o(odning)c(som)c(sidste)i(skridt)g(i)e(deres)h (algoritme.)382 1358 y FE(K)n(onklusion)382 1533 y FJ(Hvis)e(vi)h (bruger)h(Huf)n(fman-k)o(odning)i(p\345)c(HTML-\002ler)f(vil)i(vi)g (opn\345)g(den)g(optimale)h(k)o(ode)g(for)382 1646 y(denne)34 b(\002l,)e(men)h(vi)g(ben)o(ytter)i(os)e(ikk)o(e)h(af)f(de)h (m\370nstre)g(som)f(optr\346der)h(i)f(HTML-\002lerne.)382 1758 y(Her)26 b(ville)h(det)g(v\346re)f(bedre)i(hvis)f(vi)f(optog)i (noget)f(som)f(HTML)f(i)g(alf)o(abetet)k(og)e(s\345)f(medtog)382 1871 y(frekv)o(ensen)g(for)e(netop)h(dette)f(m\370nster)-5 b(.)523 1984 y(M\370nstre)33 b(optr\346der)g(ikk)o(e)f(kun)g(i)f (HTML-\002ler)l(,)f(og)h(dette)i(har)f(skabt)g(beho)o(v)o(et)h(for)f (an-)382 2097 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FA(gzip)f FJ(p\345)h(258)i(te)o(gn)e([16)r(,)f(s.)h (149].)382 4601 y FE(De)g(k)o(odede)f(symboler)382 4775 y FJ(LZ77)27 b(erstatter)k(te)o(gnene)f(med)e(k)o(odede)i(symboler)g (der)e(best\345r)i(af)e(tre)h(dele:)g(afstanden)i(fra)382 4888 y(det)d(nuv\346rende)i(punkt)f(til)f(et)g(m\370nster)h(der)f (passer)h(l\346ngere)g(tilbage)h(i)d(dataene,)j(l\346ngden)382 5001 y(af)36 b(m\370nstret)i(og)e(endelig)i(det)f(n\346ste)g(te)o(gn,)f (dvs.)h(det)g(te)o(gn)f(der)h(k)o(ommer)g(lige)g(efter)g(det)382 5114 y(m\370nster)28 b(der)f(er)g(ble)n(v)o(et)h(erstattet.)g (Afstanden)h(er)e(be)o(gr\346nset)h(af)f(st\370rrelsen)j(af)c (s\370gedelen,)382 5227 y(mens)h(l\346ngden)h(er)f(be)o(gr\346nset)h (af)f(st\370rrelsen)i(af)e(indl\346sningsdelen.)k(Man)c(kan)g(opf)o (atte)i(et)382 5340 y(k)o(odet)c(symbol)f(som)f(en)h(tre-tuppel)i(i)d (form)h(af)f(\(afstand,)i(l\346ngde,)f(n\346ste)g(te)o(gn\).)1831 5652 y(30)p eop %%Page: 31 33 31 32 bop 1079 228 a FI(Kapitel)24 b(5:)g(Analyse)g(af)g(k)o 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b(hv)n(or)e(man)e(reserv)o(erer)j(en)d(ekstra) i(bit)f(til)g(hv)o(er)f(byte)i(for)e(at)h(angi)n(v)o(e)g(om)f(det)h(er) 382 1451 y(en)f(tuppel)i(eller)g(et)e(te)o(gn.)382 1697 y FE(Gennemgang)g(af)g(eksempel)382 1871 y FJ(I)g(v)n(ores)i(eksempel) 382 2059 y Fv(

)o(Te)o(st)p 1429 2077 5 19 v 1433 2077 37 5 v 1470 2077 5 19 v 54 w(a)o(f)p 1592 2077 V 1597 2077 37 5 v 1633 2077 5 19 v 54 w(en)p 1756 2077 V 1761 2077 37 5 v 1797 2077 5 19 v 54 w(HT)o(ML)o(-s)o(id)o(e)o()382 2247 y FJ(\002ndes)f(der)g (ikk)o(e)h(m\370nstre)g(st\370rre)g(end)f(6)g(te)o(gn,)f(men)h (m\370nstret)h Fv(HTML>)c FJ(\002ndes)j(b\345de)h(i)e(slut-)382 2360 y(ningen)32 b(og)f(i)f(be)o(gyndelsen)k(af)c(\002len,)g(s\345)h (vi)g(v\346lger)g(st\370rrelsen)i(af)e(s\370gedelen)i(til)e(at)f (v\346re)382 2472 y(p\345)i(63)g(te)o(gn)g(og)g(indl\346sningsdelen)k (til)c(7)f(te)o(gn.)h(Disse)g(kan)g(beskri)n(v)o(es)i(med)d (henholdsvis)382 2585 y Fr(log)499 2607 y Ft(2)554 2585 y Fr(64)c(=)f(6)e FJ(bit)g(og)g Fr(log)1188 2607 y Ft(2)1242 2585 y Fr(8)j(=)f(3)e FJ(bit.)g(En)f(tre-tuppel)k(vil)d(derfor)h (v\346re)f(p\345)g Fr(6)d(+)g(3)g(+)f(8)27 b(=)f(17)382 2698 y FJ(bit)33 b(s\345)g(hv)o(er)g(tuppel)i(skal)e(i)g(gennemsnit)i (erstatte)g(3)d(eller)i(\003ere)e(te)o(gn)i(\(24)f(bit\))g(for)h(at)e (v)n(o-)382 2811 y(res)f(k)o(ompression)j(skal)d(kunne)h(betale)g(sig.) f(Se)f(tabel)h(5.5)g(p\345)g(n\346ste)g(side)g(for)g(skridtene)i(i)382 2924 y(algoritmen.)523 3037 y(De)25 b(f\370rste)i(seks)f(tupler)h (best\345r)g(blot)g(af)e(enk)o(eltte)o(gn,)j(og)e(det)g(f\370rste)h (interessante)i(sk)o(er)d(i)382 3150 y(linje)j(7)e(n\345r)h(algoritmen) j(l\346ser)d(et)f(m\370nster)i(der)g(kan)f(\002ndes)g(i)g (s\370gedelen.)i(Her)e(\002ndes)g(`<')382 3263 y(seks)34 b(pladser)h(fra)f(det)g(aktuelle)h(te)o(gn,)f(men)f(da)h(der)g(ikk)o(e) g(er)f(\003ere)h(te)o(gn)f(der)h(passer)h(med)382 3376 y(m\370nstret)e(bli)n(v)o(er)e(l\346ngden)i(kun)f(1)f(og)g(n\346ste)h (te)o(gn)f(`b'.)g(Herefter)i(hopper)g(algoritmen)g(s\345)382 3489 y(o)o(v)o(er)23 b(`b')h(da)g(det)g(allerede)h(er)e(ble)n(v)o(et)i (beskre)n(v)o(et.)523 3602 y(Hvis)i(der)h(er)f(\003ere)f(m\370nstre)j (der)e(passer)l(,)i(v\346lges)f(det)f(l\346ngst)h(mulige)g (naturligvis,)i(og)382 3714 y(hvis)f(der)f(er)g(\003ere)f(af)h(samme)g (l\346ngde,)h(v\346lges)f(det)h(l\346ngst)f(v\346k)g(for)g(at)g (forenkle)i(algorit-)382 3827 y(men.)523 3940 y(V)-12 b(ores)22 b(eksempel)h(ender)g(med)e(at)g(bli)n(v)o(e)h(til)f(29)h (tupler)-5 b(.)22 b(Da)f(hv)o(er)h(tuppel)g(best\345r)h(af)e(17)h(bit,) 382 4053 y(f\345r)31 b(vi)g(i)f(alt)h(493)g(bit)g(data)g(ud)g(af)g (LZ77,)f(mod)g(424)i(bit)f(f\370r)g(k)o(ompression.)i(Dette)e (h\346nger)382 4166 y(sammen)25 b(med)g(at)g(v)n(ores)i(eksempel)g (best\345r)f(af)f(sm\345)g(m\370nstre)h(der)g(kun)g(gentages)h(f\345)e (gange.)382 4279 y(T)l(uplerne)i(optager)h(simpelthen)g(for)f(me)o(get) f(plads,)g(17)h(bit,)e(i)h(forhold)i(til)e(de)g(oprindelige)j(8)382 4392 y(bit)24 b(n\345r)f(der)h(ikk)o(e)h(bli)n(v)o(er)f(sparet)h(mere)e (p\345)h(m\370nstre)g(der)g(gentager)i(sig)e(selv)-6 b(.)382 4638 y FE(LZSS)21 b(\226)i(tilstandsskift)382 4812 y FJ(Hvis)f(vi)g(i)f(stedet)i(ha)n(vde)h(ben)o(yttet)f (tilstandsskift)j(i)c(form)g(af)f(LZSS,)e(kunne)24 b(vi)e(ha)n(v)o(e)g (reduce-)382 4925 y(ret)27 b(tuplernes)i(st\370rrelse,)g(men)e(det)g (kr\346v)o(er)g(til)g(geng\346ld)i(at)d(vi)h(lader)h(dem)f(best\345)h (af)f(et)f(helt)382 5038 y(antal)31 b(byte)g(for)f(at)g(kunne)i(angi)n (v)o(e)f(om)f(en)g(gi)n(v)o(en)h(byte)g(er)f(en)g(tuppel)i(eller)f(ej.) f(Da)f(vi)h(ikk)o(e)382 5151 y(skal)e(ha)n(v)o(e)g(n\346ste)f(te)o(gn)h (med,)e(kan)i(vi)f(klare)h(os)g(med)e Fr(6)e(+)e(3)33 b(=)f(9)27 b FJ(bit)g(som)g(oprundet)j(gi)n(v)o(er)382 5264 y(16)24 b(bit)f(pr)-5 b(.)23 b(tuppel,)i(mens)f(enk)o(eltte)o(gn)i (stadig)f(vil)f(fylde)g(8)f(bit.)1831 5652 y(31)p eop %%Page: 32 34 32 33 bop 1079 228 a FI(Kapitel)24 b(5:)g(Analyse)g(af)g(k)o (ompressionsmetoder)p 382 266 2989 4 v 516 1094 2722 8 v 1665 1199 a FJ(s\370gedel)p 1992 1233 4 113 v 2150 1233 V 263 w(indl\346sningsdel)140 b(symbol)p 516 1253 2722 5 v 1992 1391 4 113 v 2046 1357 a Fv(<)p 2150 1391 V 102 w(HTML>)p FJ(...)212 b(\(0,)23 b(0,)g(L\))1670 1922 y Fv()p 2150 1956 V 102 w(<)p FJ(...)214 b(\(0,)23 b(0,)g(>\))1615 2035 y Fv()p 1992 2069 V 101 w(<)p 2150 2069 V 102 w(body>

T)p FJ(...)217 b(\(0,)23 b(0,)g(o\))1452 2261 y Fv(

Te)p FJ(...)217 b(\(0,)23 b(0,)g(d\))1397 2374 y Fv(

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Test)p FJ(...)217 b(\(6,)23 b(2,)g(p\))1179 2599 y Fv()p 2150 2633 V 102 w(Test)p 2428 2618 5 19 v 2433 2618 37 5 v 2470 2618 5 19 v 55 w(af)p FJ(...)212 b(\(9,)23 b(1,)g(T\))1070 2712 y Fv(T)p 1992 2746 4 113 v 97 w(e)p 2150 2746 V 102 w(st)p 2318 2730 5 19 v 2323 2730 37 5 v 2360 2730 5 19 v 55 w(af)p 2483 2730 V 2488 2730 37 5 v 2525 2730 5 19 v 55 w(e)p FJ(...)219 b(\(0,)24 b(0,)e(e\))1015 2825 y Fv(

)o(Te)p 1992 2859 4 113 v 97 w(s)p 2150 2859 V 102 w(t)p 2263 2843 5 19 v 2268 2843 37 5 v 2305 2843 5 19 v 55 w(af)p 2428 2843 V 2433 2843 37 5 v 2470 2843 5 19 v 55 w(en)p FJ(...)222 b(\(0,)23 b(0,)g(s\))961 2938 y Fv(T)o(es) p 1992 2972 4 113 v 97 w(t)p 2150 2972 V 2208 2956 5 19 v 2213 2956 37 5 v 2250 2956 5 19 v 157 w(af)p 2373 2956 V 2378 2956 37 5 v 2415 2956 5 19 v 55 w(en)p 2538 2956 V 2543 2956 37 5 v 2580 2956 5 19 v 55 w FJ(...)227 b(\(0,)23 b(0,)g(t\))906 3051 y Fv(

)o(Te)o(st)p 1992 3085 4 113 v 2051 3069 5 19 v 2056 3069 37 5 v 2093 3069 5 19 v 2150 3085 4 113 v 254 w(af)p 2318 3069 5 19 v 2323 3069 37 5 v 2360 3069 5 19 v 55 w(en)p 2483 3069 V 2488 3069 37 5 v 2525 3069 5 19 v 55 w(H)p FJ(...)212 b(\(0,)23 b(0,)p 3086 3069 V 3091 3069 37 5 v 3128 3069 5 19 v 78 w(\))852 3164 y Fv(T)o(es)o(t)p 1899 3182 V 1903 3182 37 5 v 1939 3182 5 19 v 1992 3198 4 113 v 152 w(a)p 2150 3198 V 102 w(f)p 2263 3182 5 19 v 2268 3182 37 5 v 2305 3182 5 19 v 55 w(en)p 2428 3182 V 2433 3182 37 5 v 2470 3182 5 19 v 55 w(HT)p FJ(...)219 b(\(0,)24 b(0,)e(a\))797 3277 y Fv(

)o(Te)o(st)p 1844 3295 V 1849 3295 37 5 v 1885 3295 5 19 v 54 w(a)p 1992 3311 4 113 v 97 w(f)p 2150 3311 V 2208 3295 5 19 v 2213 3295 37 5 v 2250 3295 5 19 v 157 w(en)p 2373 3295 V 2378 3295 37 5 v 2415 3295 5 19 v 55 w(HTM)p FJ(...)224 b(\(0,)24 b(0,)f(f\))743 3390 y Fv(T)o(es)o(t)p 1789 3408 V 1794 3408 37 5 v 1830 3408 5 19 v 54 w(af)p 1992 3424 4 113 v 2051 3408 5 19 v 2056 3408 37 5 v 2093 3408 5 19 v 2150 3424 4 113 v 254 w(en)p 2318 3408 5 19 v 2323 3408 37 5 v 2360 3408 5 19 v 55 w(HTML)p FJ(...)219 b(\(3,)24 b(1,)e(e\))633 3503 y Fv(

T)o(es)o(t)p 1680 3521 V 1685 3521 37 5 v 1721 3521 5 19 v 54 w(af)p 1844 3521 V 1849 3521 37 5 v 1885 3521 5 19 v 54 w(e)p 1992 3537 4 113 v 97 w(n)p 2150 3537 V 2208 3521 5 19 v 2213 3521 37 5 v 2250 3521 5 19 v 157 w(HTML-s)p FJ(...)217 b(\(0,)23 b(0,)g(n\))565 3616 y(...)p Fv(HTML>

)o(Te)o(st)p 1626 3634 V 1630 3634 37 5 v 1667 3634 5 19 v 54 w(a)o(f)p 1789 3634 V 1794 3634 37 5 v 1830 3634 5 19 v 54 w(en)p 1992 3649 4 113 v 2051 3634 5 19 v 2056 3634 37 5 v 2093 3634 5 19 v 2150 3649 4 113 v 254 w(HTML-si)p FJ(...)207 b(\(6,)23 b(1,)g(H\))565 3728 y(...)p Fv(ML>

Te)o(st)p 1517 3747 5 19 v 1521 3747 37 5 v 1558 3747 5 19 v 54 w(a)o(f)p 1680 3747 V 1685 3747 37 5 v 1721 3747 5 19 v 54 w(en)p 1844 3747 V 1849 3747 37 5 v 1885 3747 5 19 v 54 w(H)p 1992 3762 4 113 v 97 w(T)p 2150 3762 V 102 w(ML-side)p FJ(...)202 b(\(25,)23 b(3,)g(-\))565 3841 y(...)p Fv(body>

Test)p 1299 3860 5 19 v 1303 3860 37 5 v 1339 3860 5 19 v 55 w(a)o(f)p 1462 3860 V 1467 3860 37 5 v 1503 3860 5 19 v 54 w(en)p 1626 3860 V 1630 3860 37 5 v 1667 3860 5 19 v 54 w(H)o(TM)o(L-)p 1992 3875 4 113 v 97 w(s)p 2150 3875 V 102 w(ide

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Test)p 1189 3972 5 19 v 1194 3972 37 5 v 1230 3972 5 19 v 55 w(af)p 1353 3972 V 1358 3972 37 5 v 1394 3972 5 19 v 54 w(en)p 1517 3972 V 1521 3972 37 5 v 1558 3972 5 19 v 54 w(H)o(TM)o(L-)o(si)p 1992 3988 4 113 v 97 w(d)p 2150 3988 V 102 w(e

Test)p 1079 4085 5 19 v 1084 4085 37 5 v 1121 4085 5 19 v 56 w(af)p 1244 4085 V 1249 4085 37 5 v 1285 4085 5 19 v 54 w(en)p 1408 4085 V 1412 4085 37 5 v 1449 4085 5 19 v 54 w(H)o(TM)o(L-)o(si)o(de)p 1992 4101 4 113 v 97 w(<)p 2150 4101 V 102 w(/p>Test)p 969 4198 5 19 v 974 4198 37 5 v 1011 4198 5 19 v 55 w(af)p 1134 4198 V 1139 4198 37 5 v 1176 4198 5 19 v 56 w(e)o(n)p 1299 4198 V 1303 4198 37 5 v 1339 4198 5 19 v 55 w(H)o(TM)o(L-)o(si)o (de)o(<)p 1992 4327 4 113 v 97 w(/)p 2150 4327 V 102 w(body><)o(/b)p 1992 4440 4 113 v 97 w(o)p 2150 4440 V 102 w(dy><)o(/b)o(od)o(y>)o()425 b FJ(\(47,)24 b(4,)f(>\))p 516 4576 2722 8 v 746 4754 a FD(T)-8 b(abel)24 b(5.5:)31 b(Skridtene)26 b(i)d(LZ77-algoritmen)j(virk)o(ende)f(p\345)f (eksemplet)1831 5652 y FJ(32)p eop %%Page: 33 35 33 34 bop 1079 228 a FI(Kapitel)24 b(5:)g(Analyse)g(af)g(k)o (ompressionsmetoder)p 382 266 2989 4 v 523 548 a FJ(Hvis)k(vi)h(igen)g (arbejder)h(v)n(ores)g(eksempel)f(igennem,)h(se)e(tabel)h(5.6,)f(bli)n 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1875 V 96 w(body\(6,2\))p 2747 1875 V 99 w FJ(\(34,)g(6\))1053 1954 y(...)p Fv(/\(24,2\)\(4,2\)\()o(34)o(,6\))p 2153 1988 V 314 w(/)p 2747 1988 V 321 w FJ(\(11,)g(1\))p 635 2011 2483 8 v 810 2189 a FD(T)-8 b(abel)24 b(5.6:)31 b(Udvalgte)25 b(skridt)g(for)f(LZSS)e(virk)o(ende)k(p\345)e(eksemplet) 523 2400 y FJ(S\345)j(vi)h(f\345r)g(nu)g(21)g(te)o(gn)h(og)f(17)g (tupler)l(,)i(sv)n(arende)g(til)e Fr(21)c Fs(\001)g Fr(8)g(+)f(17)i Fs(\001)e Fr(16)35 b(=)e(440)c FJ(bit.)f(Ud)382 2513 y(o)o(v)o(er)h(dette)h(skal)f(der)g(medtages)i(en)e(ekstra)h (tilstandsbit)i(for)d(hv)o(er)h(byte,)f(hvilk)o(et)i(i)d(praksis)382 2626 y(oms\346ttes)c(til)f(en)g(byte)h(mere)f(pr)-5 b(.)22 b(8)h(byte)h(k)o(omprimeret)h(data)f(\226)f(i)f(eksemplet)j(bli)n(v)o (er)f(dette)g(til)382 2739 y Fr(7)g Fs(\001)f Fr(8)33 b(=)f(56)c FJ(bit.)g(Alts\345)f(en)h(total)g(st\370rrelse)i(p\345)d (496)h(bit,)g(hvilk)o(et)h(f)o(aktisk)h(er)d(en)g(for\370gelse)j(i)382 2852 y(forhold)24 b(til)f(LZ77.)f(Dette)h(sk)o(yldes)h(dog)f(at)g(vi)g (ikk)o(e)g(udn)o(yttede)i(de)e(16)g(bit)g(pr)-5 b(.)22 b(tuppel)j(idet)e(de)382 2965 y(7)g(bit)h(af)f(dem)g(blot)i(ble)n(v)f (brugt)g(som)g(fyld.)523 3078 y(P\345)c(trods)j(af)e(spildet)h(k)o(om)g (dette)g(eksempel)g(allige)n(v)o(el)h(t\346t)e(p\345)g(LZ77)f(hvilk)o (et)j(ud)f(o)o(v)o(er)f(de)382 3191 y(mindre)28 b(resulterende)i (symboler)f(ogs\345)f(sk)o(yldes)g(at)f(m\345den)h(m\370nstre)g (erstattes)h(p\345)e(i)g(LZSS)382 3304 y(ikk)o(e)d(er)g(s\345)g (tilb\370jeligt)i(til)e(at)f(bryde)i(m\370nstre,)g(som)e(det)h(f.eks.)g (kunne)h(ses)f(i)f(de)h(sidste)h(linjer)382 3416 y(v)o(ed)30 b(tabellen)j(for)e(LZ77.)e(Her)h(ble)n(v)h(algoritmen)h(n\370dt)g(til)e (at)h(tage)g(`b')f(med)h(i)e(den)i(tredje-)382 3529 y(sidste)21 b(tuppel)f(hv)n(orv)o(ed)i(vi)d(mistede)h(muligheden)i(for)e(at)f (erstatte)i(det)f(6)f(te)o(gn)g(lange)i(m\370nster)382 3642 y(fra)j(be)o(gyndelsen)i(af)e(eksemplet)h(og)f(m\345tte)f (n\370jes)i(med)e(5)h(te)o(gn.)382 3888 y FE(Re)o(v)o(ersibilitet)382 4062 y FJ(K)m(ompression)j(med)e(LZ77)f(gi)n(v)o(er)h(en)g(r\346kk)o(e) h(tupler)g(som)f(blot)g(kan)h(indl\346ses)g(enk)o(eltvis)i(og)382 4175 y(k)o(on)l(v)o(erteres)22 b(til)d(almindelige)i(data.)e(Hvis)f(en) h(tuppel)h(best\345r)g(af)f(\(0,)f(0,)g Fu(t)p FJ(\),)g(skri)n(v)o(es)i (blot)f(te)o(gnet)382 4288 y Fu(t)p FJ(,)29 b(ellers)i(hentes)g (f\370rst)g(det)f(angi)n(vne)i(m\370nster)f(og)f(inds\346ttes)h(hv)n (orefter)i(det)d(ekstra)h(te)o(gn)f(i)382 4401 y(tuplen)d(kan)e (tilf\370jes.)i(V)-10 b(ed)25 b(LZSS)e(fore)o(g\345r)j(det)g(tilsv)n (arende)i(idet)e(man)f(dog)h(skal)g(holde)g(styr)382 4514 y(p\345)j(om)f(en)g(byte)i(er)e(en)h(del)g(af)f(en)h(tuppel)h (eller)f(et)g(te)o(gn)g(for)g(sig.)f(Ordbogen)j(er)d(s\345)h(de)f(data) 382 4627 y(man)23 b(re)o(genererer)j(og)e(bli)n(v)o(er)g(v)o(ed)g(k)o (omprimeringen)j(opbygget)f(underv)o(ejs.)382 4873 y FE(Optimale)d(data)382 5047 y FJ(Eksemplet)28 b(indeholder)i(mange)d (tupler)i(der)e(kun)g(erstatter)i(\351t)e(te)o(gn,)g(hv)n(ad)h(der)f (er)g(uheldigt)382 5160 y(for)36 b(k)o(ompressionens)41 b(ef)n(fekti)n(vitet.)d(V)-10 b(ed)36 b(lidt)h(st\370rre)g (datam\346ngder)h(bli)n(v)o(er)f(disse)h(tupler)382 5273 y(igen)e(erstattet)h(med)e(st\370rre)i(tupler)f(hv)n(orv)o(ed)h(dette)f (problem)h(mindsk)o(es.)g(Dette)e(fremg\345r)382 5386 y(ogs\345)24 b(i)f(slutningen)k(af)c(eksemplerne.)1831 5652 y(33)p eop %%Page: 34 36 34 35 bop 1079 228 a FI(Kapitel)24 b(5:)g(Analyse)g(af)g(k)o (ompressionsmetoder)p 382 266 2989 4 v 523 548 a FJ(St\370rrelsen)33 b(af)e(s\370gedelen)j(og)e(indl\346sningsdelen)j(h\346nger)d(n\370je)g (sammen)g(med)f(hv)n(or)382 661 y(godt)f(LZ77)e(k)o(omprimerer)l(,)j (og)e(er)g(typisk)h(det)f(man)g(v\346lger)g(som)g(parameter)i(til)e (sit)g(k)o(om-)382 774 y(pressionsprogram.)37 b(St\370rre)32 b(s\370gedel)j(gi)n(v)o(er)d(mulighed)i(for)f(bedre)h(k)o(ompression)h (da)d(ord-)382 887 y(bogen)e(er)f(st\370rre)h(og)f(der)g(dermed)h(er)f (\003ere)g(muligheder)i(for)e(at)g(\002nde)g(gentagne)i(m\370nstre,)382 1000 y(men)25 b(samtidig)i(skal)g(den)f(s\370ges)h(igennem)g(fra)e (ende)i(til)f(anden,)g(og)g(dette)h(har)f(en)f(ef)n(fekt)i(p\345)382 1112 y(hastigheden)33 b(af)d(algoritmen.)h(Desuden)g(skal)g(vi)e(bruge) i(st\370rre)g(tal)f(til)g(at)f(referere)j(til)d(ord-)382 1225 y(bogen)34 b(med,)f(og)g(st\370rre)h(tal)f(betyder)h(mere)f(data.) g(V)-10 b(ed)33 b(for\370gelse)i(af)e(indl\346sningsdelens)382 1338 y(st\370rrelse)28 b(for\370ger)g(vi)e(ogs\345)h(datam\346ngden,)h (men)e(s\370getiden)j(bli)n(v)o(er)e(f)o(aktisk)h(mindre)f(fordi)382 1451 y(algoritmen)j(i)e(v\346rste)h(f)o(ald)g(stopper)h (m\370nsters\370gningen)j(p\345)28 b(samme)g(tid)g(og)h(i)f(bedste)h(f) o(ald)382 1564 y(kan)e(f)o(ange)h(l\346ngere)g(m\370nstre.)f(Et)f (langt)i(m\370nster)f(der)g(bli)n(v)o(er)h(delt)f(op,)g(betyder)h(jo)f (at)f(hele)382 1677 y(s\370gedelen)g(skal)e(s\370ges)h(igennem)g(en)e (ekstra)i(gang.)523 1790 y(Man)18 b(kan)h(dog)g(\002nde)g(optimale)h (st\370rrelser)h(for)d(hv)o(er)h(del,)g(men)f(dette)h(kr\346v)o(er)g (foranalyse)382 1903 y(af)25 b(dataene,)i(og)e(en)g(s\345dan)h (foranalyse)i(tager)e(l\346ngere)g(tid)g(end)f(at)g(k)o(omprimere)i (dem)e(fordi)382 2016 y(den)31 b(kr\346v)o(er)f(at)g(man)g(f\370rst)h (skal)g(k)o(omprimere)h(dataene)g(uden)f(be)o(gr\346nsning)i(p\345)d (hv)o(er)h(del)382 2129 y(for)24 b(s\345)f(bagefter)j(at)d(\002nde)h (de)f(maksimale)i(v\346rdier)f(for)g(afstand)h(og)f(l\346ngde.)523 2242 y(Det)h(gi)n(v)o(er)g(sig)g(selv)h(at)f(hvis)g(data)h(kun)g (best\345r)g(af)f(et)f(enk)o(elt)j(m\370nster)l(,)f(gentaget)h(mange) 382 2355 y(gange,)c(s\345)f(k)o(omprimerer)i(LZ77)d(rigtigt)j(godt,)e (men)g(hv)n(ordan)j(h\346nger)e(dette)g(sammen)f(med)382 2467 y(entropien)k(for)e(dataene?)523 2580 y(V)-5 b(i)32 b(s\345)h(i)g(afsnittet)i(om)e(Huf)n(fman-k)o(odning)k(at)c(data)h(hv)n (or)g(hv)o(ert)g(symbol)h(har)e(samme)382 2693 y(frekv)o(ens)g(k)o (omprimeres)g(d\345rligt)g(med)e(Huf)n(fman-k)o(odning.)k(Hvis)c(vi)g (nu)h(igen)g(antager)h(at)382 2806 y(v)n(ores)22 b(data)f(har)h(denne)g (e)o(genskab,)g(men)f(at)g(dataene)h(danner)h(m\370nstre.)e(Hvis)g (f.eks.)g(dataene)382 2919 y(best\345r)34 b(af)f Fu(x)786 2933 y Ft(1)825 2919 y Fu(x)877 2933 y Ft(2)916 2919 y Fu(x)968 2933 y Ft(3)1008 2919 y Fu(x)1060 2933 y Ft(4)1099 2919 y Fu(x)1151 2933 y Ft(5)1223 2919 y FJ(gentaget)i(10)e(gange,)g (s\345)g(har)g(disse)h(data)f(f\370rn\346vnte)i(e)o(genskab,)382 3032 y(men)19 b(allige)n(v)o(el)i(kan)e(dette)h(k)o(omprimeres)i(med)d (LZ77.)f(V)-5 b(i)18 b(f\345r)h(nemlig)h(\(0,)f(0,)f Fu(x)2894 3046 y Ft(1)2934 3032 y FJ(\))g(op)h(til)h(\(0,)f(0,)382 3145 y Fu(x)434 3159 y Ft(5)473 3145 y FJ(\))f(og)g(derefter)j(\(5,)d (44,)g Fu(x)1229 3159 y Ft(5)1268 3145 y FJ(\),)g(dog)g(afh\346ngigt)j (af)d(hv)n(or)h(stor)g(indl\346sningsdelen)k(er)-5 b(.)18 b(Grunden)382 3258 y(til)27 b(at)f(dette)i(kan)g(lade)f(sig)g(g\370re,) h(er)e(at)h(hvis)h(l\346ngdefeltet)h(er)e(st\370rre)h(end)f (afstandsfeltet)k(s\345)382 3371 y(gentages)22 b(symbolerne)g(fra)d (s\370gedelen)j(indtil)f(man)e(n\345r)h(op)g(p\345)f(l\346ngdefeltets)k (v\346rdi.)c(V)-5 b(i)19 b(har)382 3484 y(alts\345)h(hermed)g(k)o (omprimeret)h(50)e(te)o(gn)h(med)f(ligelig)h(frekv)o(ensfordeling)25 b(ned)19 b(til)g(6)g(tupler)i(der)382 3597 y(hv)o(er)j(kan)g(beskri)n (v)o(es)h(med)f Fr(3)c(+)g(6)h(+)f(8)25 b(=)g(17)f FJ(bit.)f(Det)g(bli) n(v)o(er)i(alts\345)f(102)g(bit)g(mod)f(400)h(bit.)523 3709 y(Dette)j(kan)h(lade)f(sig)h(g\370re)f(fordi)h(LZ77)f(arbejder)i (p\345)e(m\370nstre,)g(alts\345)h(strenge)h(af)e(sym-)382 3822 y(boler)l(,)d(hv)n(or)h(Huf)n(fman)e(arbejder)j(p\345)d(enk)o (elte)j(symboler)-5 b(.)24 b(M\370nstret)h Fu(x)2641 3836 y Ft(1)2681 3822 y Fu(x)2733 3836 y Ft(2)2772 3822 y Fu(x)2824 3836 y Ft(3)2863 3822 y Fu(x)2915 3836 y Ft(4)2955 3822 y Fu(x)3007 3836 y Ft(5)3069 3822 y FJ(bli)n(v)o(er)f (jo)382 3935 y(gentaget)31 b(ofte,)f(frekv)o(ensen)h(er)e(f)o(aktisk)i (1,)e(og)g(har)g(dermed)h(et)f(la)n(vt)h(informationsindhold)382 4048 y(s\345)23 b(det)h(kan)g(k)o(omprimeres.)523 4161 y(Det)32 b(skal)h(dog)g(n\346vnes)g(at)g(man)f(kan)h(opn\345)g(det)g (samme)f(med)g(Huf)n(fman)g(blot)i(v)o(ed)e(at)382 4274 y(lade)c(ens)f(alf)o(abet)i(best\345)f(af)f(dette)h(m\370nster)l(,)h (se)e(f.eks.)g(eksemplet)i(i)e(afsnit)h(4.1)f(p\345)g(side)h(17.)382 4387 y(Men)g(generelt)j(kr\346v)o(er)e(dette)h(igen)f(en)g(foranalyse)i (af)e(dataene.)h(I)e(stedet)i(er)e(det)h(popul\346rt)382 4500 y(med)g(en)h(k)o(ombination)j(af)c(de)h(to)f(metoder)-5 b(.)31 b(Man)e(lader)i(f\370rst)f(dataene)i(gennemg\345)f(LZ77-)382 4613 y(k)o(ompression)k(og)c(dern\346st)i(Huf)n(fman-k)o(odning,)i (netop)e(for)f(at)g(opn\345)h(den)f(optimale)h(k)o(od-)382 4726 y(ning.)24 b(Eksempler)h(p\345)e(dette)i(er)e FA(gzip)f FJ(og)i FA(zip)e FJ([16)q(,)g(s.)h(149].)382 4975 y Fw(5.2.2)99 b(Lempel-Zi)o(v)26 b(78)382 5149 y FJ(LZ78)j(ben)o(ytter)j(sig)e(af)f (en)h(seperat)i(ordbog)g([16)q(],)d(dvs.)h(at)g(der)g(ikk)o(e)g(er)g (noget)h(der)f(slettes)382 5262 y(i)25 b(ordbogen)i(efterh\345nden)i (som)c(man)g(k)o(omprimerer)i(\002len.)e(Dette)g(be)n(virk)o(er)i(at)e (m\370nstre)i(fra)382 5375 y(starten)c(af)e(\002len)g(stadig)h(kan)g (genk)o(endes)i(i)d(slutningen)j(af)d(\002len,)g(men)g(g\370r)g(at)g (ordbogen)j(som)1831 5652 y(34)p eop %%Page: 35 37 35 36 bop 1079 228 a FI(Kapitel)24 b(5:)g(Analyse)g(af)g(k)o (ompressionsmetoder)p 382 266 2989 4 v 382 548 a FJ(re)o(gel)i(bli)n(v) o(er)h(me)o(get)f(stor)g(og)h(dermed)f(g\370r)h(s\370gningstiden)j(og)c (k)o(ompressionstiden)31 b(st\370rre.)382 661 y(Desuden)25 b(tilf\370jer)g(LZ78)e(ikk)o(e)h(m\370nstre)h(til)e(ordbogen)j(p\345)e (helt)g(samme)f(m\345de)h(som)f(LZ77.)523 774 y(Ligesom)32 b(LZ77)f(erstatter)i(LZ78)e(m\370nstre)i(med)e(tupler)l(,)i(dog)f (drejer)h(det)f(sig)g(om)f(to-)382 887 y(tupler)k(der)g(indeholder)i (et)e(indeks)g(til)g(ordbogen)i(og)d(det)h(n\346ste)f(te)o(gn.)h (Sidstn\346vnte)h(har)382 1000 y(samme)18 b(form\345l)i(som)e(i)g(LZ77) g(og)h(tilsv)n(arende)i(\002ndes)e(der)g(ogs\345)h(v)n(arianter)g(der)f (ikk)o(e)h(arbejder)382 1112 y(p\345)k(denne)h(m\345de.)e(Umiddelbart)i (kunne)g(man)f(tro)g(at)f(man)h(sparer)h(plads)f(i)g(forhold)h(til)f (LZ77)382 1225 y(n\345r)32 b(der)g(kun)g(er)g(2)f(felter)l(,)i(men)f (da)g(ordbogen)i(som)e(n\346vnt)g(tit)g(bli)n(v)o(er)g(me)o(get)g(stor) l(,)g(bli)n(v)o(er)382 1338 y(indeksnumrene)24 b(tilsv)n(arende)g (store)e(og)f(kr\346v)o(er)g(dermed)h(ogs\345)f(\003ere)g(bit)g(pr)-5 b(.)20 b(m\370nster)-5 b(.)22 b(S\345)e(en)382 1451 y(LZ78-tuppel)25 b(kan)f(godt)h(bli)n(v)o(e)e(st\370rre)i(end)f(en)g(LZ77-tuppel.)523 1564 y(LZ78)e(fungerer)i(v)o(ed)e(at)h(et)f(te)o(gn)g Fu(c)1617 1578 y Ft(1)1679 1564 y FJ(indl\346ses)h(og)g(ledes)g(efter)g (i)f(ordbogen.)j(Hvis)d(te)o(gnet)382 1677 y(ikk)o(e)28 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Fo(n)1123 2242 y FJ(.)f(Endelig)h(inds\346ttes)i(dette)e(n)o(ye)g (m\370nster)g(i)f(ordbogen.)523 2355 y(Det)33 b(ses)h(at)f(ordbogen)j (hurtigt)f(kan)f(bli)n(v)o(e)f(me)o(get)h(stor)l(,)g(men)f(da)g(man)g (ikk)o(e)i(beh\370)o(v)o(er)382 2467 y(at)30 b(sende)h(den)f(med,)g(se) f(afsnit)j(5.2.2)e(p\345)g(den)g(f\370lgende)i(side,)e(er)g(dette)h(i)e (sig)i(selv)f(ikk)o(e)h(et)382 2580 y(problem,)24 b(bortset)i(fra)d(ef) n(fekten)i(p\345)f(k)o(omprimeringstiden)k(og)c(RAM)e(forbruget.)382 2823 y FE(Gennemgang)h(af)g(eksempel)382 2998 y FJ(T)m(il)29 b(at)i(illustrere)h(LZ78)e(bruger)i(vi)e(igen)h(v)n(ores)h(eksempel;)g (de)f(f\370rste)g(skridt)h(er)e(vist)h(i)f(ta-)382 3111 y(bel)24 b(5.2.2.)f(Resten)h(af)g(tabellen)h(kan)f(ses)g(i)f(bilag)h (A.2.1)f(p\345)h(side)g(67.)p 1296 3231 1138 8 v 1346 3336 a(ordbog)140 b(tuppel)125 b(m\370nster)p 1296 3390 1138 5 v 1346 3494 a Fv(1:)54 b(<)153 b(\(0,<\))217 b(<)1346 3607 y(2:)54 b(H)153 b(\(0,H\))217 b(H)1346 3720 y(3:)54 b(T)153 b(\(0,T\))217 b(T)1346 3833 y(4:)54 b(M)153 b(\(0,M\))217 b(M)1346 3946 y(5:)54 b(L)153 b(\(0,L\))217 b(L)1346 4059 y(6:)54 b(>)153 b(\(0,>\))217 b(>)1346 4172 y(7:)54 b(<)97 b(\(6,<\))190 b(><)1346 4736 y(12:p)152 b(\(0,p\))217 b(p)1346 4849 y(13:>T)97 b(\(6,T\))190 b(>T)1346 4962 y(14:e)152 b(\(0,e\))217 b(e)p 1296 5019 1138 8 v 850 5197 a FD(T)-8 b(abel)23 b(5.7:)32 b(De)22 b(f\370r)o(ste)j(skridt)g(i) e(LZ78)g(virk)o(ende)i(p\345)f(eksemplet)523 5403 y FJ(De)e(f\370rste)i (te)o(gn)f(bli)n(v)o(er)g(blot)g(erstattet)i(med)d(tupler)i(af)f (formen)g(\(0,)f Fu(t)p FJ(\),)g(men)g(anden)i(gang)1831 5652 y(35)p eop %%Page: 36 38 36 37 bop 1079 228 a FI(Kapitel)24 b(5:)g(Analyse)g(af)g(k)o (ompressionsmetoder)p 382 266 2989 4 v 382 548 a FJ(`<')k(bli)n(v)o(er) g(fundet,)h(i)f(linje)g(7,)g(kan)g(de)g(to)g(te)o(gn)g(`<')g(og)g(`b')g (erstattes)i(med)d(tuplen)j(\(1,b\))e(og)382 661 y(inds\346ttes)d(som)e (et)h(m\370nster)g(p\345)g(to)f(te)o(gn)h(i)f(ordbogen.)382 899 y FE(Re)o(v)o(ersibilitet)382 1074 y FJ(Ud)30 b(fra)i(tuplerne)h (er)e(det)g(muligt)h(at)f(genskabe)j(ordbogen)g(underv)o(ejs)f(og)e (dermed)h(f\345)f(den)382 1187 y(oprindelige)f(tekst)d(tilbage)h(uden)f (at)g(sende)g(ordbogen)i(med.)d(F)o(or)g(hv)o(er)h(tuppel)g(l\346ses)g (f\370rst)382 1300 y(indekset)f(\226)e(hvis)g(det)g(er)g(et)g(nul,)g (inds\346ttes)h(te)o(gnet)g(i)f(tuplen)h(direkte)h(i)d(ordbogen)j(og)e (indg\345r)382 1412 y(desuden)g(som)e(en)g(del)g(af)g(den)h(f\346rdige) g(tekst.)f(Hvis)g(det)g(er)g(forsk)o(elligt)j(fra)e(nul,)f(\002ndes)g (f\370rst)382 1525 y(det)29 b(m\370nster)g(som)g(indekset)h(sv)n(arer)g (til,)e(og)h(s\346ttes)g(sammen)g(med)f(te)o(gnet,)h(hv)n(orefter)i (den)382 1638 y(f\346rdige)h(streng)g(inds\346ttes)g(i)f(ordbogen)i(og) e(i)f(den)h(f\346rdige)h(tekst.)g(Hvis)e(man)h(nummere-)382 1751 y(rer)h(felterne)i(i)d(ordbogen)j(p\345)e(samme)g(m\345de)g(som)g (v)o(ed)g(k)o(omprimeringen,)i(opn\345s)g(s\345)d(den)382 1864 y(oprindelige)c(tekst.)523 1977 y(Der)20 b(er)h(dog)h(en)f(vigtig) h(forsk)o(el)h(p\345)e(k)o(ompression)j(og)d(dek)o(ompression.)j(Man)d (skal)h(nem-)382 2090 y(lig)28 b(ikk)o(e)g(s\370ge)g(i)f(ordbogen)j(v)o (ed)d(dek)o(ompression,)k(blot)d(foretage)i(et)d(opslag,)i(og)e(dette)i (g\370r)382 2203 y(dek)o(ompression)e(v\346sentligt)f(hurtigere)g(end)e (k)o(ompression.)382 2441 y FE(Optimale)f(data)382 2616 y FJ(Ligesom)i(LZ77)e(arbejder)j(LZ78)e(med)g(m\370nstre,)h(men)f (ordbogen)i(er)f(anderledes)i(indrettet)382 2729 y(idet)e(n)o(ye)f (m\370nstre)h(kun)g(tilf\370jes)g(et)f(bogsta)n(v)j(ad)d(gangen,)h(hv)n (ad)g(der)f(for\345rsager)j(at)d(LZ78)f(er)382 2842 y(langsommere)28 b(til)f(at)f(tilpasse)i(sig)e(sandsynligheder)32 b(for)26 b(dataene.)i(S\345)e(LZ78)f(virk)o(er)j(bedst)382 2954 y(p\345)k(st\370rre)h(m\346ngder)f(ensartede)j(data)d(hv)n(or)h (m\370nstrene)h(kan)f(n\345)f(at)f(k)o(omme)h(i)g(ordbogen.)382 3067 y(Dette)21 b(kan)h(v\346re)f(problematisk)k(i)20 b(forbindelse)25 b(med)c(HTML-\002ler)f(der)h(som)g(vi)h(har)f(set)h(i) f(be-)382 3180 y(ho)o(vsanalysen,)30 b(kan)e(v\346re)f(forholdsvist)k (sm\345)26 b(\226)h(desuden)i(kan)f(der)f(optr\346de)i(sm\345)d(blokk)o (e,)382 3293 y(f.eks.)e(lister)l(,)g(med)g(me)o(get)g(ensartet)h (materiale)g(i)e(HTML-\002lerne,)g(og)h(her)g(vil)g(LZ78)f(s\345)g(mu-) 382 3406 y(ligvis)i(ikk)o(e)f(kunne)h(n\345)f(at)f(tilpasse)i(sig.)523 3519 y(Ligesom)39 b(v)o(ed)f(LZ77)f(er)h(der)h(ble)n(v)o(et)g (opfundet,)h(endog)f(endnu)h(\003ere,)e(v)n(arianter)i(p\345)382 3632 y(LZ78.)c(V)-10 b(ariationerne)40 b(\346ndrer)e(bl.a.)f(p\345)g (hv)n(or)h(mange)g(te)o(gn)f(der)h(tilf\370jes)h(til)e(genk)o(endte)382 3745 y(m\370nstre)22 b(v)o(ed)g(hv)o(er)f(forek)o(omst)i(og)f(hv)n (ordan)h(ordbogen)h(opretholdes)g(og)e(s\370ges)g(i.)f(Desuden)382 3858 y(er)i(der)h(v)n(arianter)i(med)d(kun)h(\351t)f(felt)h(i)f(hv)o (er)h(tuppel.)523 3971 y(Et)35 b(eksempel)i(p\345)f(denne)h(v)n(ariant) g(kaldes)g(LZW)c(\(efter)k(T)-7 b(.)34 b(W)-7 b(elch)36 b([16)q(,)f(s.)g(123]\))i(og)382 4084 y(bruger)31 b(en)e(speciel)i 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)o(Te)o(st)p 1697 2327 V 1701 2327 37 5 v 1738 2327 5 19 v 54 w(a)o(f)p 1860 2327 V 1865 2327 37 5 v 1901 2327 5 19 v 54 w(en)p 2024 2327 V 2029 2327 37 5 v 2065 2327 5 19 v 54 w(HT)o(ML)o(-s)o(id)o(e)o(<)o(p>T)o(es) o(t)p 1642 2439 V 1647 2439 37 5 v 1683 2439 5 19 v 54 w(af)p 1806 2439 V 1810 2439 37 5 v 1847 2439 5 19 v 54 w(e)o(n)p 1970 2439 V 1974 2439 37 5 v 2010 2439 5 19 v 55 w(H)o(TM)o(L-)o(si)o(de)o(<)o(/b)o(od)o(y>)o()o(Te)o(st)p 1588 2552 V 1592 2552 37 5 v 1629 2552 5 19 v 54 w(a)o(f)p 1751 2552 V 1756 2552 37 5 v 1792 2552 5 19 v 54 w(en)p 1915 2552 V 1920 2552 37 5 v 1956 2552 5 19 v 54 w(HT)o(ML)o(-s)o(id)o(e<)o(/p>)o (<)o(/HT)o(M)432 2647 y(><)o(p>)o(Tes)o(t)p 1533 2665 V 1538 2665 37 5 v 1574 2665 5 19 v 54 w(af)p 1697 2665 V 1701 2665 37 5 v 1738 2665 5 19 v 54 w(e)o(n)p 1860 2665 V 1865 2665 37 5 v 1901 2665 5 19 v 54 w(HTM)o(L-)o(si)o(de)o (<)o(/b)o(od)o(y>)o('.)f(T)-7 b(allet)19 b(16)i(ud)f(for)g(`>')g(angi)n(v)o(er)h(at)f(den)g(16.)g(r\346kk)o(e)g (i)g(den)g(roterede)i(tabel)382 4965 y(startede)32 b(med)e(`>'.)h(Husk) f(p\345)h(at)f(vi)g(ikk)o(e)i(la)n(v)o(ede)f(om)f(p\345)h(linjerne,)h (vi)e(\003yttede)h(dem)g(blot.)382 5078 y(Det)e(sidste)h(bogsta)n(v)h (i)e(denne)h(r\346kk)o(e)g(m\345)e(pga.)h(roteringen)j(imidlertid)f (v\346re)e(det)h(bogsta)n(v)382 5191 y(der)d(stod)h(lige)g(f\370r)f (`>',)g(og)h(da)f(vi)g(i)g(de)g(k)o(odede)i(data)f(har)f(gemt)g(alle)h (de)f(sidste)i(bogsta)n(v)o(er)g(i)382 5303 y(r\346kk)o(erne,)h (\002nder)f(vi)f(v)o(ed)h(r\346kk)o(e)g(16)g(i)f(tabellen)i(bogsta)n(v) o(et)h(f\370r)e(`>',)g(nemlig)g(`L)-8 b('.)27 b(F)o(or)h(`L)-8 b(')1831 5652 y(38)p eop %%Page: 39 41 39 40 bop 1079 228 a FI(Kapitel)24 b(5:)g(Analyse)g(af)g(k)o (ompressionsmetoder)p 382 266 2989 4 v 382 464 2991 8 v 437 587 5 19 v 442 587 37 5 v 479 587 5 19 v 487 568 a Fv(HTML-side

)o()o()o(<)o(p>)o(Te)o(st)p 3006 587 V 3010 587 37 5 v 3047 587 5 19 v 54 w(a)o(f)p 3170 587 V 3174 587 37 5 v 3210 587 5 19 v 55 w(e)o Fg(n)p 437 699 V 442 699 37 5 v 479 699 5 19 v 487 681 a Fv(af)p 602 699 V 607 699 37 5 v 644 699 5 19 v 55 w(en)p 767 699 V 772 699 37 5 v 809 699 5 19 v 55 w(HTML-si)o(de)o(<)o(/b)o(od)o(y>)o ()o(<)o(bo)o(dy)o(><)o(p>)o(Tes)o Fg(t)p 437 812 V 442 812 37 5 v 479 812 5 19 v 487 794 a Fv(en)p 602 812 V 607 812 37 5 v 644 812 5 19 v 55 w(HTML-side<)o(/p)o(><)o(/H)o(TML)o(><)o(HT)o(ML)o(><)o (bod)o(y>)o(T)o(es)o(t)p 3170 812 V 3174 812 37 5 v 3210 812 5 19 v 55 w(a)o Fg(f)432 907 y Fv(-side

)o ()o(<)o(bo)o(dy)o(><)o(p>)o(Tes)o(t)p 2733 925 V 2738 925 37 5 v 2774 925 5 19 v 54 w(af)p 2897 925 V 2901 925 37 5 v 2938 925 5 19 v 54 w(e)o(n)p 3060 925 V 3065 925 37 5 v 3101 925 5 19 v 54 w(HTM)o Fg(L)432 1020 y Fv(/HTML><)o(p>)o(Te)o(st)p 1806 1038 V 1810 1038 37 5 v 1847 1038 5 19 v 54 w(a)o(f)p 1970 1038 V 1974 1038 37 5 v 2010 1038 5 19 v 55 w(e)o(n)p 2133 1038 V 2138 1038 37 5 v 2174 1038 5 19 v 54 w(HT)o(ML)o(-s)o(ide)o ()o()o Fg(<)432 1133 y Fv(/body><)o(HT)o (ML>)o()o(Te)o(st)p 2188 1151 V 2192 1151 37 5 v 2229 1151 5 19 v 54 w(a)o(f)p 2351 1151 V 2356 1151 37 5 v 2392 1151 5 19 v 54 w(en)p 2515 1151 V 2520 1151 37 5 v 2556 1151 5 19 v 54 w(HT)o(ML)o(-s)o(id)o(e<)o(/p>)o Fg(<)432 1246 y Fv(/p>)o(<) o(p>)o(Te)o(st)p 2406 1264 V 2410 1264 37 5 v 2447 1264 5 19 v 54 w(a)o(f)p 2570 1264 V 2574 1264 37 5 v 2610 1264 5 19 v 55 w(e)o(n)p 2733 1264 V 2738 1264 37 5 v 2774 1264 5 19 v 54 w(HT)o(ML)o(-s)o(ide)o Fg(<)432 1359 y Fv(<)o(bo)o(dy>)o(T)o(es)o(t)p 1860 1377 V 1865 1377 37 5 v 1901 1377 5 19 v 54 w(af)p 2024 1377 V 2029 1377 37 5 v 2065 1377 5 19 v 54 w(en)p 2188 1377 V 2192 1377 37 5 v 2229 1377 5 19 v 54 w(H)o(TM)o(L-)o(sid)o(e<)o (/p)o(><)o(/b)o(ody)o Fg(>)432 1472 y Fv()o(<)o(bo)o(dy)o(><)o(p>T)o(es)o(t)p 2242 1490 V 2247 1490 37 5 v 2283 1490 5 19 v 54 w(af)p 2406 1490 V 2410 1490 37 5 v 2447 1490 5 19 v 54 w(e)o(n)p 2570 1490 V 2574 1490 37 5 v 2610 1490 5 19 v 55 w(H)o(TM)o(L-)o(si)o(de)o()1866 1564 y FJ(.)1866 1598 y(.)1866 1631 y(.)432 1744 y Fv(ody>)o(T)o(est)p 2079 1762 V 2083 1762 37 5 v 2120 1762 5 19 v 54 w(a)o(f)p 2242 1762 V 2247 1762 37 5 v 2283 1762 5 19 v 54 w(en)p 2406 1762 V 2410 1762 37 5 v 2447 1762 5 19 v 54 w(H)o(TML)o(-s)o(id)o (e<)o(/p)o(>

Test)p 1042 1875 V 1047 1875 37 5 v 1083 1875 5 19 v 55 w(af)p 1206 1875 V 1210 1875 37 5 v 1247 1875 5 19 v 54 w(e)o(n)p 1370 1875 V 1374 1875 37 5 v 1410 1875 5 19 v 55 w(H)o(TM)o(L-)o(si)o (de)o(<)o(/b)o(od)o(y>)o()o(<)o Fg(b)432 1970 y Fv(p>)o(<)o(bo)o(dy)o(>T)o(es)o(t)p 2351 1988 V 2356 1988 37 5 v 2392 1988 5 19 v 54 w(af)p 2515 1988 V 2520 1988 37 5 v 2556 1988 5 19 v 54 w(en)p 2679 1988 V 2683 1988 37 5 v 2720 1988 5 19 v 54 w(H)o(TM)o(L-)o(si)o(de<)o Fg(/)432 2083 y Fv(p>Test)p 767 2101 V 772 2101 37 5 v 809 2101 5 19 v 55 w(af)p 932 2101 V 937 2101 37 5 v 974 2101 5 19 v 56 w(en)p 1097 2101 V 1101 2101 37 5 v 1138 2101 5 19 v 54 w(H)o(TM)o(L-s)o(id)o(e<)o(/p)o(><)o(/bo)o(dy)o(><)o(/H)o(TM)o (L><)o(HT)o(ML)o(><)o(bo)o(dy>)o Fg(<)432 2195 y Fv(side

<)o(/HT)o(ML)o(><)o(HT)o(ML)o(>)o(T)o(est)p 2679 2214 V 2683 2214 37 5 v 2720 2214 5 19 v 54 w(a)o(f)p 2842 2214 V 2847 2214 37 5 v 2883 2214 5 19 v 54 w(en)p 3006 2214 V 3010 2214 37 5 v 3047 2214 5 19 v 54 w(H)o(TML)o Fg(-)432 2308 y Fv(st)p 547 2327 V 552 2327 37 5 v 589 2327 5 19 v 55 w(af)p 712 2327 V 717 2327 37 5 v 754 2327 5 19 v 55 w(en)p 877 2327 V 882 2327 37 5 v 919 2327 5 19 v 55 w(HTML-)o(si)o(de<)o(/p)o(><)o(/b)o(od)o(y><)o(/H)o(TM)o (L>)o(<)o(bo)o(dy)o(><)o(p>T)o Fg(e)432 2421 y Fv(t)p 492 2439 V 497 2439 37 5 v 534 2439 5 19 v 55 w(af)p 657 2439 V 662 2439 37 5 v 699 2439 5 19 v 55 w(en)p 822 2439 V 827 2439 37 5 v 864 2439 5 19 v 55 w(HTML-s)o(id)o(e)o(<)o(HT)o (ML>)o()o(Te)o Fg(s)432 2534 y Fv(y><)o(bod)o(y>)o(T)o(es)o(t)p 1970 2552 V 1974 2552 37 5 v 2010 2552 5 19 v 55 w(a)o(f)p 2133 2552 V 2138 2552 37 5 v 2174 2552 5 19 v 54 w(en)p 2297 2552 V 2301 2552 37 5 v 2338 2552 5 19 v 54 w(H)o(TM)o(L-s)o(id)o(e<)o(/p)o (><)o(/bo)o Fg(d)432 2647 y Fv(y>

Test)p 932 2665 V 937 2665 37 5 v 974 2665 5 19 v 56 w(af)p 1097 2665 V 1101 2665 37 5 v 1138 2665 5 19 v 54 w(e)o(n)p 1260 2665 V 1265 2665 37 5 v 1301 2665 5 19 v 54 w(HTM)o(L-)o(si)o(de)o(<) o(/b)o(od)o(y>)o()o()o()208 b FJ(14)p 1432 1551 V 214 w(26:)c Fv(T)k FJ(29)p 2318 1551 V 214 w(44:)c Fv(e)j FJ(40)674 1630 y(9:)226 b Fv(>)208 b FJ(15)p 1432 1664 V 214 w(27:)c Fv(T)k FJ(30)p 2318 1664 V 214 w(45:)c Fv(b)j FJ(34)652 1743 y(10:)c Fv(e)208 b FJ(39)p 1432 1777 V 214 w(28:)c Fv(T)k FJ(31)p 2318 1777 V 214 w(46:)c Fv(b)j FJ(35)652 1856 y(11:)c Fv(>)208 b FJ(16)p 1432 1890 V 214 w(29:)c Fv(H)k FJ(20)p 2318 1890 V 214 w(47:)c Fv(/)230 b FJ(7)652 1969 y(12:)203 b Fv(>)208 b FJ(17)p 1432 2003 V 214 w(30:)c Fv(H)k FJ(21)p 2318 2003 V 214 w(48:)c Fv(<)j FJ(13)652 2082 y(13:)c Fv(>)208 b FJ(18)p 1432 2116 V 214 w(31:)c Fv(H)k FJ(22)p 2318 2116 V 214 w(49:)c Fv(-)230 b FJ(4)652 2195 y(14:)203 b Fv(y)208 b FJ(52)p 1432 2229 V 214 w(32:)c Fv(>)k FJ(19)p 2318 2229 V 214 w(50:)c Fv(e)j FJ(41)652 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b(eksemplet)j(fr)o(a)d(Burr)l(ows-Wheeler)n(-)382 2317 y(tr)o(ansformationen)382 2583 y FE(Eksempel)382 2758 y FJ(Grundet)30 b(det)g(store)g(alf)o(abet)h(har)e(vi)g(kun)h(vist)g (det)f(f\370rste)i(udsnit)f(af)f(alf)o(abetet.)i(T)-7 b(abel)30 b(5.11)382 2871 y(viser)24 b(de)f(f\370rste)i(12)e(skridt)i (i)e(en)g(mo)o(v)o(e-to-front-k)o(odning)29 b(p\345)23 b(de)h(data)g(vi)f(\002k)f(v)o(ed)i(Burro)n(ws-)382 2983 y(Wheeler)n(-transformation)q(en,)29 b(alts\345)24 b(den)g(sidste)h(k)o (olonne)h(i)d(tabel)h(5.9.)523 3096 y(Som)19 b(det)i(ses)g(til)f (sidst,)h(gi)n(v)o(er)g(mo)o(v)o(e-to-front)i(sm\345)d(v\346rdier)h (n\345r)g(symbolerne)i(optr\346der)382 3209 y(i)d(grupper)l(,)i (ogs\345)f(selv)h(om)d(der)i(k)o(ommer)g(et)f(`e')g(ind)h(mellem)g (gruppen)h(af)e(`>'.)g(Dette)h(er)f(hv)n(ad)382 3322 y(der)h(skaber)h(den)f(sk\346v)o(e)g(sandsynlighedsfor)q(del)q(ing)27 b(som)20 b(Huf)n(fman-k)o(odning)k(kan)e(udn)o(ytte.)382 3566 y FE(Re)o(v)o(ersibilitet)382 3740 y FJ(V)-5 b(i)28 b(f\345r)h(alts\345)h(en)f(talr\346kk)o(e)h(v)o(ed)g(mo)o(v)o (e-to-front-k)o(odning,)k(men)29 b(vi)g(skal)h(desuden)h(gemme)382 3853 y(det)e(oprindelige)i(alf)o(abet)f(for)f(at)f(kunne)i(gendanne)h (de)d(oprindelige)k(data.)d(Dette)f(kan)h(blot)382 3966 y(g\370res)k(som)e(en)g(streng)i(af)f(symboler)l(,)h(og)f(det)g(k)o (ommer)f(dermed)i(til)e(at)h(fylde)g(det)g(samme)382 4079 y(som)23 b(l\346ngden)i(af)e(alf)o(abetet.)523 4192 y(V)-5 b(i)21 b(starter)i(med)f(at)g(opskri)n(v)o(e)i(det)e(samme)g (alf)o(abet)i(som)e(vi)g(startede)i(med)e(v)o(ed)g(k)o(odning.)382 4305 y(Dern\346st)31 b(henter)i(vi)e(de)h(f\370rste)g(nummer)g(fra)f(k) o(oden,)i(henter)g(symbolet)f(der)g(er)f(p\345)h(denne)382 4417 y(position)25 b(i)e(alf)o(abetet)i(og)e(nedskri)n(v)o(er)i(dette)f (symbol.)g(Symbolet)f(skal)h(s\345)f(ligesom)h(v)o(ed)f(k)o(od-)382 4530 y(ning,)e(\003yttes)g(frem)f(i)g(alf)o(abetet.)j(Dern\346st)e (g\370r)g(vi)f(det)h(samme)f(med)h(n\346ste)g(tal)f(i)g(k)o(oden.)i (Man)382 4643 y(kan)i(f)o(aktisk)i(g\370re)e(n\370jagtigt)i(dette)f(v)o (ed)f(at)g(betragte)h(tabel)g(5.11,)f(og)g(s\345)f(blot)i(opf)o(atte)g (k)o(oden)382 4756 y(som)e(den)h(gi)n(vne.)382 5003 y Fw(5.3.3)99 b(K)n(onklusion)382 5177 y FJ(Burro)n(ws-Wheeler)n (-transformati)q(on)q(en)38 b(resulterer)c(i)e(mange)g(ens)h(te)o(gn)f (t\346t)g(p\345)g(hinanden,)382 5290 y(og)25 b(mo)o(v)o(e-to-front)j (transformerer)h(dette)d(til)f(en)h(sekv)o(ens)h(hv)n(or)f(forek)o (omsten)j(af)c(sm\345)g(v\346r)n(-)382 5403 y(dier)32 b(er)f(stor)h(i)f(forhold)i(til)e(store)h(v\346rdier)-5 b(.)32 b(H\370j)f(sandsynlighed)36 b(for)31 b(nogle)i(v\346rdier)l(,)f (lille)1831 5652 y(41)p eop %%Page: 42 44 42 43 bop 1079 228 a FI(Kapitel)24 b(5:)g(Analyse)g(af)g(k)o (ompressionsmetoder)p 382 266 2989 4 v 382 548 a FJ(for)h(andre)g(er)g (s\345)f(de)h(ideelle)h(data)f(til)g(Huf)n(fman-k)o(odning,)j(og)c (denne)i(form)f(for)g(k)o(omprime-)382 661 y(ring)36 b(med)f(Burro)n(ws-Wheeler)n(-transformati)q(one)q(n,)40 b(dern\346st)d(mo)o(v)o(e-to-front)g(og)f(til)f(sidst)382 774 y(Huf)n(fman-k)o(odning)27 b(ben)o(yttes)e(i)e(programmet)i FA(bzip2)d FJ([18)q(].)523 887 y(Man)i(opn\345r)h(ikk)o(e)g(ret)f(me)o (get)h(v)o(ed)f(at)g(bruge)h(Burro)n(ws-Wheeler)n(-transformati)q(on)q (en)30 b(og)382 1000 y(mo)o(v)o(e-to-front)23 b(hv)o(er)e(for)f(sig.)h (Burro)n(ws-Wheeler)n(-transformatio)q(ne)q(n)26 b(\003ytter)20 b(kun)h(rundt)h(p\345)382 1112 y(bogsta)n(v)o(erne)30 b(i)25 b(dataene)k(og)d(tilf\370jer)i(et)e(tal,)g(og)h(mo)o(v)o (e-to-front)i(er)d(kun)h(n)o(yttig)g(at)f(bruge)i(p\345)382 1225 y(me)o(get)23 b(specielle)j(typer)f(af)e(data.)h(Men)f(tilsammen)i (er)e(de)h(an)l(v)o(endelige.)523 1338 y(Det)h(er)h(dog)h(umiddelbart)h (sv\346rere)f(at)f(udtale)h(sig)f(om)f(hv)n(or)i(me)o(get)f(plads)h (det)f(er)g(n\370d-)382 1451 y(v)o(endigt)k(at)d(bruge)j(for)e(et)g(gi) n(v)o(ent)h(m\370nster)g(i)f(mods\346tning)h(til)g(de)f (ordbogsbaserede)33 b(algo-)382 1564 y(ritmer)-5 b(.)34 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b(Der)e(kan)g(dog)h(desuden)h(v\346re)e(et)g(problem)h(med)f(den)g (typisk)o(e)i(st\370rrelse)g(af)382 2580 y(en)21 b(HTML-\002l)f(\226)h (hvis)h(de)g(er)f(for)h(sm\345,)f(kan)h(Burro)n(ws-Wheeler)n (-transformat)q(ion)q(en)27 b(vise)c(sig)382 2693 y(at)g(v\346re)h(for) f(d\345rlig)i(i)e(forhold)j(til)d(en)h(ordbogsbaseret)k(algoritme.)1831 5652 y(42)p eop %%Page: 43 45 43 44 bop 382 1171 a FC(Kapitel)43 b(6)382 1586 y FK(Udv\346lgelse)53 b(af)f(algoritme)382 2031 y FJ(V)-5 b(i)31 b(har)i(i)g(de)f(fore)o (g\345ende)k(kapitler)f(foretaget)g(unders\370gelser)h(der)e(kan)f (bruges)h(til)f(at)g(op-)382 2144 y(stille)d(kra)n(v)g(til)f(den)g (algoritme)i(som)d(bruges)j(til)e(at)g(k)o(omprimere)h(HTML-\002lerne,) e(samt)h(at)382 2257 y(belyse)37 b(hv)n(ordan)g(eksisterende)i (algoritmer)e(fungerer)-5 b(.)37 b(Ud)d(fra)h(dette)h(kan)g(vi)f (fors\370ge)i(at)382 2369 y(sammens\346tte)27 b(en)e(\226)g(teoretisk)j (set)e(\226)f(bedre)i(l\370sning)g(end)g(blot)f(de)f(eksisterende)30 b(generelle)382 2482 y(algoritmer)-5 b(.)28 b(En)e(efterf\370lgende)k (implementering)g(og)d(test)g(vil)f(s\345)h(vise)g(om)f(vi)h(har)f (gjort)i(de)382 2595 y(rigtige)d(slutninger)-5 b(.)523 2708 y(V)g(i)17 b(indleder)j(kapitlet)g(med)e(en)g(gennemgang)i(af)e (hv)n(ad)h(man)f(kan)g(k)o(omprimere)i(i)d(HTML.)382 2821 y(Herefter)36 b(diskuterer)i(vi)d(hv)n(orvidt,)i(og)e(hv)n (orledes)j(dette)e(kan)g(implementeres.)h(V)-5 b(i)34 b(f)o(andt)382 2934 y(desuden)29 b(i)d(kapitel)j(3)e(ud)g(af)g(at)f(v)n (ores)j(algoritme)f(ikk)o(e)g(kun)g(skal)f(kunne)i(k)o(omprimere)f (sta-)382 3047 y(tisk)h(HTML,)d(men)i(ogs\345)h(dynamisk)i(HTML,)25 b(og)k(dette)g(stiller)h(nogle)g(ekstra)g(kra)n(v)f(til)f(den)382 3160 y(algoritme)33 b(vi)f(v\346lger)-5 b(.)32 b(Algoritmen)h(skal)f (v\346re)g(s\345)f(hurtig)i(at)e(den)i(i)e(v\346rste)h(tilf\346lde)g (kan)382 3273 y(k)o(omprimerere)26 b(dynamisk)o(e)f(HTML-\002ler)d(hv)o (er)i(gang)g(de)g(bli)n(v)o(er)g(hentet.)382 3565 y FB(6.1)119 b(Hv)o(ad)30 b(kan)g(k)n(omprimer)n(es)g(i)g(HTML?)382 3772 y FJ(I)37 b(HTML)d(\002ndes)k(redundans)i(og)d(en)g(forudsigelig)k (struktur)e(\226)e(be)o(gge)h(kan)g(udn)o(yttes)h(til)382 3885 y(k)o(ompression.)26 b(F)-7 b(.eks.)23 b(skri)n(v)o(es)h(HTML)d (mindst)j(to)g(gange)g(i)f(en)g(HTML-\002l,)e(i)i(det)h(f\370rste)h (tag)382 3998 y(og)31 b(i)f(det)h(sidste.)h(Derudo)o(v)o(er)g(\002ndes) f(der)g(ting)h(der)f(kan)g(forudsiges)j(v)o(ed)d(brug)h(af)e(mindre)382 4111 y(information.)c(Et)c(eksempel)j(p\345)f(dette)g(er)f(`<')h(og)g (`>',)f(der)h(er)f(o)o(v)o(er\003\370dige)i(hvis)f(man)f(v)o(ed)h(at) 382 4224 y(man)29 b(har)g(at)f(g\370re)i(med)f(et)f(tag)h(\226)g(dette) h(kunne)g(g\370res)g(v)o(ed)f(at)g(indf\370re)h(et)f(\003ag)f(foran)i (hv)o(ert)382 4337 y(skift.)25 b(Desuden)g(\002ndes)g(der)f(tags)h(som) f(kun)h(er)f(gyldige)i(hvis)f(de)f(st\345r)h(indenfor)h(andre)g(tags.) 382 4450 y(Et)c(eksempel)k(p\345)d(dette)i(er)e(\204\223)i(som)e (kun)h(kan)g(st\345)g(inden)g(for)g(\204\223.)523 4563 y(Der)c(er)h(derfor)h(\003ere)e(m\370nstre)i(man)f(b\370r)g(kunne) h(udn)o(ytte)g(i)e(HTML)f(til)h(at)h(frembringe)i(en)382 4676 y(bedre)j(k)o(ompression.)h(Dette)e(kunne)h(til)e(dels)h(v\346re)g (v)o(ed)g(at)f(forarbejde)j(HTML-\002len)d(inden)382 4789 y(k)o(ompression)33 b(eller)f(v)o(ed)e(at)h(la)n(v)o(e)g(en)g(n)o (y)f(k)o(ompressionsalgoritme,)36 b(som)30 b(er)h(optimeret)h(til)382 4901 y(m\370nstre)25 b(i)e(HTML)e(\002ler)-5 b(.)523 5014 y(V)g(i)24 b(har)h(p\345)g(den)h(baggrund)h(v)n(algt)f(at)f (belyse)i(tre)e(metoder)h(som)f(umiddelbart)i(kan)f(v\346re)382 5127 y(oplagte)f(til)f(k)o(ompression)i(af)e(HTML:)518 5340 y Fs(\017)46 b FJ(Dynamisk)25 b(ordbogsskift)1831 5652 y(43)p eop %%Page: 44 46 44 45 bop 1237 228 a FI(Kapitel)25 b(6:)e(Udv\346lgelse)i(af)f (algoritme)p 382 266 2989 4 v 518 548 a Fs(\017)46 b FJ(\306ndring)25 b(af)e(alf)o(abetet)j(s\345)e(det)g(indeholder)i(tags) 518 736 y Fs(\017)46 b FJ(Opdeling)25 b(af)f(\002lerne)g(s\345)f(at)g (tags)i(og)e(tekst)i(k)o(omprimeres)g(hv)o(er)f(for)g(sig)523 948 y(V)-5 b(i)28 b(vil)i(i)g(det)g(f\370lgende)i(uddybe)f(de)f(tre)g (o)o(v)o(enst\345ende)j(metoder)e(og)e(designe)j(en)e(algo-)382 1061 y(ritme)24 b(til)f(k)o(omprimering)j(af)d(HTML-\002ler)-5 b(.)382 1354 y FB(6.2)119 b(Dynamisk)30 b(ordbog)382 1561 y FJ(En)e(m\345de)i(at)f(udn)o(ytte)i(forek)o(omster)g(af)f(ord)f (og)h(bogsta)n(v)o(er)h(p\345)f(er)f(v)o(ed)g(at)g(ben)o(ytte)i(en)e (ord-)382 1674 y(bogsbaseret)j(algoritme)d(hv)n(or)h(man)e(dog)h (skifter)g(ordbog)h(dynamisk.)g(V)-5 b(i)27 b(forestiller)k(os)d(at)382 1786 y(man)23 b(de\002nerer)i(en)e(r\346kk)o(e)h(n\370gleord)h(som)e (for\345rsager)j(et)d(ordbogsskift)k(hv)o(er)d(gang)g(de)f(m\370-)382 1899 y(des.)h(Dette)h(kunne)h(v\346re)e(ord)h(som)f(\204table\223,)i (\204font\223)g(og)e(\204script\223,)i(hv)n(or)g(de)e(parametre)i(som) 382 2012 y(optr\346der)33 b(i)e(tag'et)h(har)g(forsk)o(ellige)j (sandsynligheder)-5 b(.)36 b(Eksempelvis)e(er)d(der)h(me)o(get)f(lille) 382 2125 y(sandsynlighed)d(for)c(at)g(\002nde)g(ordet)h(\204size\223)g (i)f(forbindelse)j(med)d(n\370gleordet)i(\204table\223,)g(mens)382 2238 y(det)e(derimod)g(er)g(me)o(get)f(sandsynligt)k(at)d(m\370de)f(i)g (forbindelse)k(med)c(n\370gleordet)k(\204font\223.)382 2487 y Fw(6.2.1)99 b(Fr)n(emgangsm\345de)382 2662 y FJ(Algoritmen)24 b(virk)o(er)g(v)o(ed)f(at)g(man)f(starter)i(med)f(at)f(bruge)i(en)f (prim\346r)g(ordbog)h(som)f(k)o(ommer)382 2774 y(til)j(at)g(indeholde)j (de)d(te)o(gn)g(og)g(ord)h(der)f(ikk)o(e)h(k)o(ommer)f(efter)h(et)f (n\370gleord.)i(N\345r)e(algoritmen)382 2887 y(m\370der)33 b(et)f(n\370gleord)j(\226)e(f.eks.)f(\204table\223)j(\226)d(skifter)i (den)f(til)g(en)f(\204table\223-ordbog)38 b(som)32 b(inde-)382 3000 y(holder)26 b(de)f(ord)g(den)h(m\370der)f(i)g(forbindelse)j(med)c (n\370gleordet.)k(N\345r)c(algoritmen)j(m\370der)f(\204>\223)382 3113 y(\(tag-slut\))36 b(skifter)f(den)g(tilbage)g(til)f(den)g (prim\346re)g(ordbog.)i(Ordbogen)f(arbejder)h(s\345ledes)382 3226 y(med)23 b(hele)h(ord,)g(s\345ledes)h(at)f(ordet)g(\204size\223)h (vil)f(indg\345)g(i)f(\204font\223-ordbogen.)523 3339 y(F)o(ordelen)k(v)o(ed)e(dette)i(ville)f(v\346re)f(at)h(de)f(parametre) i(som)f(ofte)g(bruges)h(i)e(et)g(bestemt)i(tag)382 3452 y(vil)c(f\345)g(la)n(v)o(ere)h(indeksnumre,)h(end)e(hvis)h(de)f(l\345)g (i)f(en)h(stor)g(ordbog.)h(Man)f(kunne)h(forestille)i(sig)382 3565 y(at)31 b(en)g(ordbog)i(for)f(n\370gleordet)i(\204table\223)f (ville)f(indeholde)i(ord)e(som)f(\204border\223,)i(\204bgcolor\223)382 3678 y(og)26 b(\204cellpadding\223)j(der)d(med)f(stor)h(sandsynlighed)k (vil)c(indg\345)h(i)e(det)g(p\345g\346ldende)j(tag.)e(Der)n(-)382 3791 y(v)o(ed)h(vil)f(der)h(i)f(de)g(k)o(omprimerede)j(data)f(indg\345) f(et)g(st\370rre)g(antal)h(la)n(v)o(e)f(indeksnumre)i(hvilk)o(et)382 3904 y(medf\370rer)24 b(en)e(sk\346v)o(ere)h(sandsynlighedsfo)q(rde)q (lin)q(g)28 b(der)23 b(kan)f(k)o(omprimeres)j(mere)d(ef)n(fekti)n(vt) 382 4016 y(med)h(f.eks.)h(Huf)n(fman-k)o(odning.)523 4129 y(Endvidere)32 b(kan)f(en)f(r\346kk)o(e)h(af)f(de)h(dynamisk)o(e)h (ordb\370ger)h(v\346re)d(indbygget)j(i)d(algorit-)382 4242 y(men.)17 b(V)-10 b(ed)18 b(at)g(gennemg\345)i(et)e(stort)h(antal) g(hjemmesider)h(og)e(at)g(gennemg\345)i(HTML-standarden)382 4355 y(kan)28 b(ordb\370gernes)k(grundl\346ggende)g(indhold)e (bestemmes.)f(Derv)o(ed)f(sparer)i(man)e(at)f(o)o(v)o(er)n(-)382 4468 y(f\370re)d(en)g(vis)f(m\346ngde)h(tekst)h(for)e(hv)o(er)h (HTML-\002l)e(der)h(o)o(v)o(erf\370res.)523 4581 y(Der)i(er)h(dog)g(et) f(problem)i(i)f(forbindelse)i(med)e(store)g(og)g(sm\345)g(bogsta)n(v)o (er)-5 b(.)27 b(Hvis)f(algorit-)382 4694 y(men)i(skal)h(k)o(ende)h (alle)f(standard-tags)k(og)28 b(deres)i(parametre)g(bli)n(v)o(er)f(det) g(i)f(sig)h(selv)g(en)f(stor)382 4807 y(m\346ngde)k(data,)g(men)g(hvis) g(der)h(derudo)o(v)o(er)h(f.eks.)e(skal)g(tages)h(h\370jde)g(for)f(at)g (ordet)h(\204size\223)382 4920 y(kan)c(optr\346de)g(i)f(alle)h(mulige)g (k)o(ombinationer)j(af)c(store)h(og)g(sm\345)f(bogsta)n(v)o(er)l(,)i (f.eks.)f(\204size\223,)382 5033 y(\204Size\223,)24 b(\204sIze\223)g (osv)-6 b(.,)24 b(bli)n(v)o(er)g(ordb\370gerne)j(for)d(store.)523 5146 y(Hvis)h(denne)i(algoritme)g(skal)e(bruges,)i(er)e(det)h(alts\345) g(n\370dv)o(endigt)i(at)d(opgi)n(v)o(e)h(kra)n(v)o(et)h(om)382 5258 y(en)37 b(totalt)h(tabsfri)g(algoritme)g(fordi)g(man)f(ville)g (v\346re)g(n\370dt)h(til)f(at)f(v\346lge)h(\351n)g(bestemt)h(af)382 5371 y(k)o(ombinationerne.)28 b(T)m(il)23 b(sidernes)j(prim\346re)e (form\345l,)g(at)f(bli)n(v)o(e)h(fremvist)h(i)f(en)f(bro)n(wser)l(,)i (ville)1831 5652 y(44)p eop %%Page: 45 47 45 46 bop 1237 228 a FI(Kapitel)25 b(6:)e(Udv\346lgelse)i(af)f (algoritme)p 382 266 2989 4 v 382 548 a FJ(der)30 b(dog)h(ikk)o(e)f(sk) o(e)h(nogen)g(\346ndring)g(fordi)g(HTML)c(ikk)o(e)k(g\370r)f(forsk)o (el)i(p\345)e(store)h(eller)f(sm\345)382 661 y(bogsta)n(v)o(er)-5 b(.)523 774 y(Dette)29 b(stiller)g(dog)g(nogle)h(st\370rre)g(kra)n(v)f (til)f(selv)o(e)i(implementeringen,)h(fordi)f(man)e(ikk)o(e)382 887 y(kan)c(tillade)i(at)e(noget)h(af)f(den)g(almindelige)j(tekst)e (bli)n(v)o(er)f(opf)o(attet)i(som)e(HTML)e(og)i(dermed)382 1000 y(bli)n(v)o(er)33 b(\346ndret.)h(Hvis)e(der)h(f.eks.)g(ble)n(v)h (\346ndret)f(i)f(Ja)n(v)n(ascript,)k(kunne)e(resultatet)h(v\346re)e(f)o (a-)382 1112 y(talt.)28 b(Derfor)h(skal)g(algoritmen)i(kunne)e(tage)g (h\370jde)h(for)f(alle)f(de)h(fejlkilder)i(der)d(kan)h(v\346re)f(i)382 1225 y(forbindelse)f(start)d(og)g(slut)g(af)f(HTML-tags.)382 1475 y Fw(6.2.2)99 b(K)n(onklusion)382 1649 y FJ(De)31 b(o)o(v)o(enst\345ende)j(o)o(v)o(erv)o(ejelser)g(viser)e(at)g(vi)f(v)o (ed)h(at)f(udn)o(ytte)i(den)f(viden)h(man)e(i)g(forv)o(ejen)382 1762 y(har)21 b(om)g(HTML-formatet)g(efter)h(alt)g(at)f(d\370mme,)g (kan)g(opn\345)h(en)g(bedre)g(k)o(ompression)i(end)e(de)382 1875 y(generelle)f(metoder)-5 b(.)21 b(Men)e(samtidig)h(kan)g(vi)f(k)o (onkludere)j(at)e(der)f(en)g(lang)h(r\346kk)o(e)g(situationer)382 1988 y(der)j(b\370r)h(o)o(v)o(erv)o(ejes)g(inden)g(en)g(e)o(gentlig)g (standard)i(kan)d(de\002neres)i(og)e(implementeres.)i(Dels)382 2101 y(kr\346v)o(er)34 b(den)g(en)f(grundig)j(unders\370gelse)h(af)d (HTML-standarden)h(og)f(af)f(hvilk)o(e)i(tags)g(der)382 2213 y(bruges)30 b(oftest,)g(men)f(der)g(skal)g(ogs\345)h(g\370res)g (nogle)g(o)o(v)o(erv)o(ejelser)h(med)e(hensyn)h(til)f(at)g(sikre)382 2326 y(at)k(metoden)i(er)f(rob)n(ust)h(nok)f(til)g(f.eks.)g(ikk)o(e)g (at)g(gi)n(v)o(e)g(problemer)h(hvis)g(der)f(er)f(sm\345)g(fejl)h(i)382 2439 y(HTML-\002lerne.)29 b(Endelig)j(kunne)f(man)f(o)o(v)o(erv)o(eje)i (at)e(bruge)h(forsk)o(ellige)j(algoritmer)e(til)e(at)382 2552 y(k)o(omprimere)25 b(de)f(forsk)o(ellige)i(dele.)523 2665 y(Alt)h(i)g(alt)h(vil)g(det)g(bli)n(v)o(e)g(for)g(omf)o(attende)i (at)e(implementere)i(o)o(v)o(enst\345ende)g(i)e(dette)g(pro-)382 2778 y(jekt,)j(idet)g(vi)f(ikk)o(e)i(har)f(den)g(forn\370dne)h(tid)f (til)g(at)f(la)n(v)o(e)h(benarbejdet)j(inden)e(den)f(e)o(gentlige)382 2891 y(implementering.)k(Derudo)o(v)o(er)f(kunne)g(man)f(forestille)i (sig)e(at)f(man)h(v)o(ed)g(simplere)h(meto-)382 3004 y(der)27 b(kunne)h(opn\345)g(n\346sten)f(liges\345)h(god)f(k)o (ompression,)j(s\345)d(vi)f(har)h(ikk)o(e)h(arbejdet)g(mere)f(med)382 3117 y(denne)e(algoritme.)382 3409 y FB(6.3)119 b(\306ndring)31 b(af)e(alfabetet)382 3616 y FJ(En)19 b(anden)j(metode)f(til)g(at)f(udn) o(ytte)i(den)f(viden)g(vi)f(i)g(forv)o(ejen)i(har)f(om)f(HTML,)e(er)i (v)o(ed)g(at)g(la)n(v)o(e)382 3729 y(en)i(v)n(ariant)h(af)f(Huf)n (fman-k)o(odning.)k(V)-10 b(arianten)23 b(skal)g(udo)o(v)o(er)g(at)f (analysere)j(hyppigheden)g(af)382 3842 y(enk)o(elte)e(bogsta)n(v)o(er)g (ogs\345)f(analysere)h(hyppigheden)h(af)d(an)l(v)o(endte)i(HTML-tags,)e (dvs.)g(at)f(den)382 3955 y(skal)k(medtage)h(en)e(forudde\002neret)k (m\346ngde)d(m\370nstre)h(i)e(alf)o(abetet.)523 4068 y(Man)d(kunne)i(p\345)e(den)h(m\345de)f(forestille)j(sig)d(at)g (m\370nstret)i(\204table\223)g(indg\345r)f(lige)g(s\345)f(hyppigt)382 4181 y(som)26 b(bogsta)n(v)o(et)j(\204q\223,)e(og)g(at)f(man)h(dermed)g (kunne)h(opn\345)g(en)e(me)o(get)h(ef)n(fekti)n(v)h(k)o(ompression)382 4294 y(af)23 b(sider)i(der)f(bruger)h(de)e(samme)g(HTML-tags)g(me)o (get,)h(hv)n(ad)g(de)f(\003este)h(jo)f(g\370r)-5 b(.)523 4407 y(Problemet)34 b(med)f(denne)i(id\351)f(er)f(at)g(det)h(er)f (tvilvsomt)i(hv)n(or)f(ef)n(fekti)n(v)h(den)f(vil)f(v\346re)g(i)382 4520 y(forhold)d(til)e(f.eks.)h(LZ77)e(og)i(derefter)h(Huf)n(fman.)e (LZ77)g(opdager)i(jo)e(m\370nstre)i(og)e(p\345)g(den)382 4633 y(m\345de)e(vil)f(et)h(ord)g(der)g(optr\346der)g(\003ere)g(gange)g (bli)n(v)o(e)g(k)o(omprimeret)i(betydeligt.)g(Derudo)o(v)o(er)382 4745 y(opf)o(anger)22 b(LZ77)c(ogs\345)i(l\346ngere)h(m\370nstre)f(end) g(blot)g(enk)o(elte)h(ord.)f(V)-12 b(ores)20 b(forslag)h(ville)f (f.eks.)382 4858 y(k)o(omprimere)31 b(\204size\223)h(godt,)e(men)g (hvis)g(\204size=2)i(f)o(ace=V)-10 b(erdana\223)33 b(optr\346der)e (mere)f(end)g(\351n)382 4971 y(gang)g(vil)g(LZ77)g(k)o(omprimere)h (hele)g(dette)g(stykk)o(e.)g(P\345)e(den)h(m\345de)g(vil)h(den)f (ogs\345)h(k)o(ompri-)382 5084 y(merere)23 b(m\370nstre)g(der)g (opst\345r)h(i)e(forbindelse)j(med)d(ofte)h(brugte)h(almindelige)h (ord.)d(V)-5 b(i)21 b(har)i(p\345)382 5197 y(den)h(baggrund)i(v)n(algt) e(ikk)o(e)h(at)e(arbejde)i(mere)f(med)f(denne)i(algoritme.)1831 5652 y(45)p eop %%Page: 46 48 46 47 bop 1237 228 a FI(Kapitel)25 b(6:)e(Udv\346lgelse)i(af)f (algoritme)p 382 266 2989 4 v 382 548 a FB(6.4)119 b(Opdeling)32 b(af)d(\002ler)n(ne)382 755 y FJ(V)-10 b(ed)22 b(at)h(dele)g (HTML-\002len)e(op)i(i)f(to)h(dele,)g(hv)n(or)h(den)f(ene)g(del)g (best\345r)h(af)e(HTML-k)o(oderne)i(og)382 868 y(den)j(anden)i(af)d (tekst,)i(kan)f(vi)g(udn)o(ytte)i(v)n(ores)f(viden)g(om)f(k)o (omprimeringsalgoritmer)32 b(til)27 b(at)382 981 y(bruge)e(de)e(mest)h (optimale)h(algoritmer)g(p\345)f(hv)o(er)f(del.)523 1094 y(V)-5 b(i)39 b(kan)j(bruge)f(LZ77)f(p\345)h(HTML-delen,)f(da)h(denne)h (er)f(hurtig)h(og)f(vil)g(f)o(ange)g(alle)382 1207 y(m\370nstre,)33 b(forudsat)h(at)d(vi)h(lader)h(s\370gedelen)i(v\346re)d(p\345)f (st\370rrelse)k(med)c(\002len.)h(Dermed)g(har)382 1319 y(vi)k(reduceret)j(redundansen)h(i)35 b(HTML-\002len.)g(Men)h (Lempel-Zi)n(v)h(77)f(kan)h(ikk)o(e)g(k)o(ompri-)382 1432 y(mere)22 b(almindeligt)i(tekst)e(n\346r)g(s\345)g(godt)g(som)g (en)f(algoritme)j(der)e(bruger)h(Burro)n(ws-Wheeler)n(-)382 1545 y(transformationen)33 b(\(dette)c(h\346nger)h(sammen)e(med)h(at)f (almindelig)j(tekst)e(har)g(\003ere)f(afh\346n-)382 1658 y(gigheder)e(te)o(gnene)f(indbyrdes)h(end)e(direkte)h(m\370nstre\).)523 1771 y(Man)d(kunne)h(bruge)h(Burro)n(ws-Wheeler)n(-transformati)q(on)q (en)k(p\345)22 b(hele)h(\002len)f(da)g(den)g(f)o(an-)382 1884 y(ger)32 b(de)f(samme)g(m\370nstre)i(som)e(LZ77,)g(dog)h(e)n(v)o (entuelt)h(undtaget)h(det)d(sidste)i(`>')f(idet)g(der)382 1997 y(kan)h(opst\345)h(forsk)o(ellige)i(k)o(ontekster)g(til)d (h\370jre)h(for)f(dette)h(te)o(gn)f(fordi)h(et)e(tag)i(kan)f (efterf\370l-)382 2110 y(ges)f(af)g(tekst)i(eller)e(et)g(andet)i(tag.)e (Men)g(en)g(algoritme)i(der)e(ben)o(ytter)i(Burro)n(ws-Wheeler)n(-)382 2223 y(transformationen)28 b(er)23 b(noget)i(langsommere)h(end)e(LZ77,) f(og)h(af)f(denne)i(grund)g(er)f(det)g(\370nsk-)382 2336 y(v\346rdigt)g(at)g(be)o(gr\346nse)h(brugen)g(til)e(der)h(hv)n(or)h (det)e(g\370r)h(mest)g(ga)n(vn.)523 2449 y(Da)17 b FA(bzip2)g FJ(k)o(omprimerer)j(vha.)f(Burro)n(ws-Wheeler)n(-transformatio)q(ne)q (n)24 b(og)18 b FA(gzip)f FJ(vha.)382 2562 y(af)23 b(LZ77,)g(beh\370)o (v)o(er)h(vi)g(ikk)o(e)g(at)f(implementere)j(disse)e(algoritmer)i(og)d (kan)h(n\370jes)h(med)e(selv)o(e)382 2674 y(opdelingen)k(og)c (sammens\346tningen)k(af)c(\002lerne.)382 2967 y FB(6.5)119 b(V)-12 b(or)n(es)29 b(algoritme)382 3174 y FJ(V)-12 b(ores)25 b(algoritme)i(skal)e(alts\345)h(dele)g(HTML-\002ler)d(op.)i 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f(er)h(`<')f(og)h FD(ErT)-8 b(ekst)25 b Fr(=)d FJ(sand)768 4888 y(s\346t)h FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(f)o(alsk)768 5001 y(tilf\370j)i FD(AntalBo)o(gstaver)j FJ(til)c FD(T)-8 b(alliste)768 5114 y FJ(s\346t)23 b FD(AntalBo)o(gstaver)29 b Fr(=)c(0)768 5227 y FJ(kald)i(O)t FH(P)t(S)t(P)t(L)t(I)t(T)t(N)t(I)t (N)t(G)t FJ(\()5 b FH(M)t(E)g(D)32 b(T)t(E)t(G)t(N)t(E)t(T)f(F)t(J)t(E) t(R)t(N)t(E)t(T)g(F)t(R)t(A)d FJ(D)q FH(A)l(T)m(A)t FJ(\))586 5340 y(ellers)d(hvis)f(n\346ste)g(te)o(gn)g(er)f(`>')h(og)g FD(ErT)-8 b(ekst)24 b Fr(=)f FJ(f)o(alsk)1831 5652 y(48)p eop %%Page: 49 51 49 50 bop 1394 228 a FI(Kapitel)24 b(7:)g(Implementering)p 382 266 2989 4 v 768 548 a FJ(s\346t)f FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(sand)768 661 y(tilf\370j)i FD(AntalBo)o(gstaver)j FJ(til)c FD(T)-8 b(alliste)768 774 y FJ(s\346t)23 b FD(AntalBo)o (gstaver)29 b Fr(=)c(0)768 887 y FJ(kald)i(O)t FH(P)t(S)t(P)t(L)t(I)t (T)t(N)t(I)t(N)t(G)t FJ(\()5 b FH(M)t(E)g(D)32 b(T)t(E)t(G)t(N)t(E)t(T) f(F)t(J)t(E)t(R)t(N)t(E)t(T)g(F)t(R)t(A)d FJ(D)q FH(A)l(T)m(A)t FJ(\))586 1000 y(ellers)d(hvis)f FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(sand)768 1112 y(tilf\370j)i(n\346ste)f(te)o(gn)g(til)f FD(T)-8 b(ekstliste)768 1225 y FJ(for\370g)25 b FD(AntalBo)o(gstaver)j FJ(med)c(1)768 1338 y(kald)j(O)t FH(P)t(S)t(P)t(L)t(I)t(T)t(N)t(I)t(N)t (G)t FJ(\()5 b FH(M)t(E)g(D)32 b(T)t(E)t(G)t(N)t(E)t(T)f(F)t(J)t(E)t(R) t(N)t(E)t(T)g(F)t(R)t(A)d FJ(D)q FH(A)l(T)m(A)t FJ(\))586 1451 y(ellers)768 1564 y(tilf\370j)d(n\346ste)f(te)o(gn)g(til)f FD(HTML-liste)768 1677 y FJ(for\370g)i FD(AntalBo)o(gstaver)j FJ(med)c(1)768 1790 y(kald)j(O)t FH(P)t(S)t(P)t(L)t(I)t(T)t(N)t(I)t(N)t (G)t FJ(\()5 b FH(M)t(E)g(D)32 b(T)t(E)t(G)t(N)t(E)t(T)f(F)t(J)t(E)t(R) t(N)t(E)t(T)g(F)t(R)t(A)d FJ(D)q FH(A)l(T)m(A)t FJ(\))586 1903 y(n\345r)c(vi)g(er)f(l\370bet)i(t\370r)e(for)h FD(Data)768 2016 y FJ(returner)i FD(HTML-liste)p FJ(,)c FD(T)-8 b(ekstliste)25 b FJ(og)f FD(T)-8 b(alliste)384 2242 y FJ(I)t FH(N)t(I)t(T)t(I)t(A)t(L) t(I)t(S)t(E)5 b(R)t(I)g(N)t(G)t FJ(:)586 2355 y(\002nd)24 b(antallet)h(af)e(elementer)j(i)d FD(T)-8 b(alliste)586 2467 y FJ(hvis)25 b(det)f(er)f(et)g(lige)h(antal)768 2580 y(s\346t)f FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(f)o(alsk)586 2693 y(ellers)768 2806 y(s\346t)g FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(sand)384 2919 y(S)t FH(A)t(M)t(L)t(I)t(N)t(G)t FJ(\()t(H)t(T)t(M)t(L)t(-)t FH(L)t(I)t(S)5 b(T)g(E)g FJ(,)33 b(T)t FH(E)t(K)t(S)t(T)t(L)t(I)t(S)t(T)t(E)5 b FJ(,)33 b(T)l FH(A)t(L)t FJ(:)t(:)t(T)l FH(A)t(L)t(L)t(I)t(S)5 b(T)g(E)g FJ(\))g(:)586 3032 y(hvis)25 b FD(ErT)-8 b(ekst)25 b Fr(=)d FJ(sand)i(og)g FD(T)-8 b(al)23 b Fr(=)i(0)768 3145 y FJ(s\346t)e FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(f)o(alsk)768 3258 y(tilf\370j)i(et)e(`>')h(til)f FD(Output)768 3371 y FJ(kald)k(S)t FH(A)t(M)t(L)t(I)t(N)t(G)t FJ(\()t(H)t(T)t(M)t(L)t(-)t FH(L)t(I)t(S)5 b(T)g(E)t FJ(,)33 b(T)t FH(E)t(K)t(S)t(T)t(L)t(I)t(S)t (T)5 b(E)g FJ(,)32 b(T)l FH(A)t(L)t(L)t(I)t(S)t(T)t(E)t FJ(\))586 3484 y(ellers)25 b(hvis)f FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(sand)768 3597 y(tilf\370j)i(det)f(nuv\346rende)h(te)o(gn)f (fra)g FD(T)-8 b(ekstliste)25 b FJ(til)e FD(Output)768 3709 y FJ(kald)k(S)t FH(A)t(M)t(L)t(I)t(N)t(G)t FJ(\()t(H)t(T)t(M)t(L)t (-)t FH(L)t(I)t(S)5 b(T)g(E)t FJ(,)33 b(T)t FH(E)t(K)t(S)t(T)t(L)t(I)t (S)t(T)5 b(E)g FJ(,)32 b(\()t(T)l FH(A)t(L)r Fs(\000)p Fr(1)r FJ(\))t(:)t(:)t(T)l FH(A)t(L)5 b(L)g(I)g(S)t(T)g(E)g FJ(\))586 3822 y(ellers)25 b(hvis)f FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(f)o(alsk)h(og)g FD(T)-8 b(al)23 b Fr(=)h(0)768 3935 y FJ(s\346t)f FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(sand)768 4048 y(tilf\370j)i(et)e(`<')h(til)f FD(Output)768 4161 y FJ(kald)k(S)t FH(A)t(M)t(L)t(I)t(N)t(G)t FJ(\()t(H)t(T)t(M)t(L)t(-)t FH(L)t(I)t(S)5 b(T)g(E)t FJ(,)33 b(T)t FH(E)t(K)t(S)t(T)t(L)t(I)t(S)t (T)5 b(E)g FJ(,)32 b(T)l FH(A)t(L)t(L)t(I)t(S)t(T)t(E)t FJ(\))586 4274 y(ellers)25 b(hvis)f FD(ErT)-8 b(ekst)25 b Fr(=)e FJ(f)o(alsk)768 4387 y(tilf\370j)i(det)f(nuv\346rende)h(te)o (gn)f(fra)g FD(HTML-liste)f FJ(til)g FD(Output)768 4500 y FJ(kald)k(S)t FH(A)t(M)t(L)t(I)t(N)t(G)t FJ(\()t(H)t(T)t(M)t(L)t(-)t FH(L)t(I)t(S)5 b(T)g(E)t FJ(,)33 b(T)t FH(E)t(K)t(S)t(T)t(L)t(I)t(S)t (T)5 b(E)g FJ(,)32 b(\()t(T)l FH(A)t(L)r Fs(\000)p Fr(1)r FJ(\))t(:)t(:)t(T)l FH(A)t(L)5 b(L)g(I)g(S)t(T)g(E)g FJ(\))586 4613 y(n\345r)24 b(b\345de)h FD(HTML-liste)e FJ(og)g FD(T)-8 b(ekstliste)25 b FJ(er)e(tomme)768 4726 y(returner)j FD(Output)523 5051 y FJ(Bem\346rk)35 b(at)g(opsplitningen) 40 b(og)c(gendannelsen)k(returnerer)e(lister)f(i)e(modsat)h(r\346kk)o (e-)382 5164 y(f\370lge)d(af)g(de)f(data)h(som)g(bli)n(v)o(er)g(gi)n(v) o(et)g(til)f(funktionen)k(som)c(parameter)-5 b(.)34 b(Dette)e(er)h (gjort)g(af)382 5277 y(hastighedsm\346ssige)e(\345rsager;)e(man)d(kan)h (nemlig)h(hurtigt)h(tilf\370je)f(et)e(element)i(til)f(en)g(liste)g(i) 382 5390 y(starten)k(af)f(listen,)h(men)e(hvis)i(man)e(skal)i (tilf\370je)g(et)e(element)i(til)f(slutningen)j(af)c(listen)i(skal)1831 5652 y(49)p eop %%Page: 50 52 50 51 bop 1394 228 a FI(Kapitel)24 b(7:)g(Implementering)p 382 266 2989 4 v 382 548 a FJ(listen)g(f)o(aktisk)g(gendannes)h(helt)f (fra)e(n)o(y)h(af.)f(Med)g(hensyn)i(til)f(k)o(ompression)i(har)e(dette) h(ingen)382 661 y(betydning)i(da)e(alle)g(m\370nstre)g(bli)n(v)o(er)h (transformeret)h(ens.)382 953 y FB(7.2)119 b(\330vrige)30 b(funktioner)382 1160 y FJ(Da)17 b(v)n(ores)j(funktioner)h(arbejder)g (p\345)d(lister)l(,)h(skal)g(vi)g(desuden)h(ha)n(v)o(e)f(funktioner)i (der)e(v)n(aretager)382 1273 y(forbindelsen)30 b(fra)c(\002ler)f(o)o(v) o(er)h(tekststrenge)k(til)c(lister)h(og)f(tilbage)i(igen,)e(for)h(at)e (kunne)j(hente)382 1386 y(og)c(gemme)f(dataene.)523 1499 y(Af)28 b(disse)h(funktioner)j(vil)d(vi)f(kun)i(beskri)n(v)o(e)g (funktionerne)i(der)d(indl\346ser)h(tallisten)h(fra)382 1612 y(tal\002len)21 b(og)f(gemmer)h(den,)g(da)f(bitoperationer)k(er)d (noget)g(indviklede)j(i)19 b(SML)g(\226)h(tallene)i(gem-)382 1725 y(mes)h(med)h(16)f(bits)h(pr\346cision)i(\(hvilk)o(et)f(sv)n(arer) 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y(for)j(k)o(omprimering)o(en)j(af)c(HTML-delen,)g Ff(bzip2)f FD(er)h(for)h(k)o(omprimering)o(en)j(af)c(tekstdelen)382 1735 y FJ(skiftene)28 b(mellem)e(tekst)h(og)g(HTML)d(v)o(ed)i(at)g (reserv)o(ere)i(en)e(ASCII-v\346rdi)g(som)g(ikk)o(e)h(bli)n(v)o(er)382 1848 y(brugt)j(i)e(HTML-\002lerne,)f(og)i(inds\346tte)h(en)e(ekstra)i (byte)f(med)f(denne)i(v\346rdi)f(alle)g(de)g(steder)382 1961 y(hv)n(or)24 b(der)g(skal)g(skiftes)i(i)d(\002lerne.)523 2074 y(Hvis)i(vi)h(ser)f(helt)h(bort)g(fra)g(tal\002len,)g(k)o (omprimerer)h(v)n(ores)g(algoritme)g(en)e(smule)h(bedre.)382 2187 y(Det)34 b(kan)h(h\346nge)h(sammen)f(med)f(at)h FA(bzip2)e FJ(bedre)j(kan)f(k)o(omprimere)h(de)f(m\370nstre)h(som)382 2300 y(\002ndes)29 b(i)f(tekstdelen)k(end)d FA(gzip)e FJ(kan,)i(men)f(det)h(kan)g(ogs\345)h(v\346re)e(fordi)i(vi)f(fjerner)h (alle)f(`>')382 2413 y(og)24 b(`<'.)523 2526 y(Der)19 b(er)g(dog)h(en)f(ulempe)h(v)o(ed)f(at)h(bruge)g(to)f(forsk)o(ellige)k (algoritmer;)e(alf)o(abetet)h(skal)d(o)o(v)o(er)n(-)382 2638 y(f\370res)26 b(to)e(gange.)i(Specielt)g(v)o(ed)f(sm\345)f (\002ler)h(udg\370r)h(alf)o(abetet)h(en)e(betydelig)i(del)f(af)e (\002lst\370rrel-)382 2751 y(sen.)j(Derudo)o(v)o(er)i(kan)e(man)g(o)o (v)o(erv)o(eje)i(om)d(der)i(er)f(nogen)i(grund)f(til)f(at)g(opdele)i (\002lerne,)f(n\345r)382 2864 y(vi)f(i)g(afsnit)h(7.5.1)f(bem\346rk)o (ede)i(at)e FA(gzip)f FJ(i)h(nogle)h(tilf\346lde)g(k)o(omprimerer)h (bedre)g(p\345)e(be)o(gge)382 2977 y(\002ler)32 b(end)i FA(bzip2)p FJ(.)d(I)h(beho)o(vsanalysen)37 b(k)o(onkluderede)g(vi)c(at) g(HTML-\002lerne)f(generelt)j(er)382 3090 y(forholdsvis)27 b(sm\345,)c(hvilk)o(et)i(igen)f(taler)h(for)e FA(gzip)p FJ(.)523 3203 y(Udf\370rselstiden)31 b(for)c(v)n(ores)h(algoritme)h(er) e(ogs\345)h(problematisk.)h(Den)e(langsomme)i(ud-)382 3316 y(f\370rselstid)k(k)o(ommer)e(fra)g(v)n(ores)h(opdelingsprogram)k (i)30 b(SML,)e(og)j(sp\370r)n(gsm\345let)j(er)c(om)h(det)382 3429 y(sk)o(yldes)25 b(en)f(d\345rlig)g(implementation)j(eller)d(om)f (det)h(er)f(en)h(d\345rlig)h(algortime.)382 3678 y Fw(7.5.4)99 b(Algoritmens)24 b(tidsk)o(ompleksitet)382 3852 y FJ(F)o(or)29 b(at)h(f\345)g(klarlagt)i(hv)n(orfor)h(v)n(ores)e(implementation)i(v)n (ar)d(s\345)g(langsom)i(under)f(testen,)h(un-)382 3965 y(ders\370ger)26 b(vi)d(om)g(det)h(er)f(selv)o(e)h(algoritmens)i (struktur)g(der)e(g\370r)g(at)f(det)h(tager)g(lang)h(tid.)523 4078 y(Dette)31 b(kan)h(teoretisk)h(tidsk)o(ompleksitet)i(sv)n(are)d (p\345)f([1)q(])f(\226)h(tidsk)o(ompleksiteten)36 b(for)31 b(en)382 4191 y(algoritme)25 b(beskri)n(v)o(er)g(forholdet)h(mellem)d (m\346ngden)h(af)f(data)h(og)g(udf\370rselstiden)j(for)d(algo-)382 4304 y(ritmen.)31 b(Man)f(beskri)n(v)o(er)i(dette)g(vha.)e(af)g Fu(O)s FJ(-notationen,)k(f.eks.)c Fu(O)s Fr(\()p Fu(n)2649 4271 y Ft(2)2689 4304 y Fr(\))p FJ(.)f(Dette)i(betyder)h(at)382 4417 y(hvis)24 b Fu(T)13 b Fr(\()p Fu(n)p Fr(\))23 b FJ(er)g(tiden)i(det)e(tager)i(at)e(udf\370re)i(en)e(funktion)j(n\345r)e (st\370rrelsen)i(af)d(dataene)j(er)d Fu(n)p FJ(,)f(s\345)382 4530 y(eksisterer)k(der)e(et)f Fu(k)j FJ(og)e(et)f Fu(n)1310 4544 y Ft(0)1372 4530 y FJ(s\345)g(for)h Fu(n)h Fs(\025)g Fu(n)1830 4544 y Ft(0)1891 4530 y FJ(g\346lder:)1585 4734 y Fu(T)13 b Fr(\()p Fu(n)p Fr(\))25 b Fs(\024)g Fu(k)s(f)10 b Fr(\()p Fu(n)p Fr(\))p Fu(;)382 4938 y FJ(hv)n(or)24 b Fu(f)10 b Fr(\()p Fu(n)p Fr(\))23 b FJ(er)g(det)h(vi)f (skri)n(v)o(er)i(i)e(O-notationen,)j(alts\345)e Fu(O)s Fr(\()p Fu(f)10 b Fr(\()p Fu(n)p Fr(\)\))p FJ(.)523 5051 y(En)27 b(operation)k(der)e(ikk)o(e)g(afh\346nger)g(st\370rrelsen)i(af) d(dataene)i(angi)n(v)o(es)g(med)e Fu(O)s Fr(\(1\))p FJ(,)g(dvs.)382 5164 y(den)g(tager)h(1)e(tidsenhed.)j(Hvis)e(man)f(har)h(\003ere)f (operationer)l(,)k(kan)d(man)g(sl\345)g(dem)f(sammen,)382 5277 y(og)33 b(resultatet)j(bli)n(v)o(er)e(blot)g(den)f(st\370rste.)i (Eksempelvis)g(hvis)f(man)f(har)h(en)f(operation)j(der)1831 5652 y(55)p eop %%Page: 56 58 56 57 bop 1394 228 a FI(Kapitel)24 b(7:)g(Implementering)p 382 266 2989 4 v 382 548 a FJ(tager)34 b Fu(O)s Fr(\(1\))f FJ(og)g Fu(O)s Fr(\()p Fu(n)p Fr(\))p FJ(,)f(s\345)h(er)g(summen)g (blot)h Fu(O)s Fr(\()p Fu(n)p Fr(\))p FJ(.)e(Desuden)i(g\346lder)g(at)f Fu(O)s Fr(\()p Fu(k)s(f)10 b Fr(\()p Fu(n)p Fr(\)\))32 b FJ(er)382 661 y(\346kvi)n(v)n(alent)25 b(med)e Fu(O)s Fr(\()p Fu(f)10 b Fr(\()p Fu(n)p Fr(\)\))23 b FJ(\226)g(en)h(k)o (onstant)i(f)o(aktor)f(har)f(ingen)g(betydning.)523 774 y(P\345)36 b(denne)i(baggrund)i(kan)d(vi)g(nu)g(analysere)j(v)n(ores)e (algoritme.)h(Da)d(vi)h(blot)g(\370nsk)o(er)382 887 y(en)28 b(\370)o(vre)h(gr\346nse)g(for)g(hv)n(or)g(lang)g(tid)g(v)n(ores)g (algoritme)h(vil)f(tage,)g(unders\370ger)i(vi)d(den)h(med)382 1000 y(hensyn)22 b(til)f(v\346rste)g(tilf\346lde.)g(De)f(f\370rste)i (funktioner)i(la)n(v)o(er)d(lister)g(om)f(til)h(strenge)h(og)f(strenge) 382 1112 y(om)j(til)h(lister)l(,)h(og)f(det)g(er)f(som)h(sagt)g(lige)o (gyldigt)j(om)c(vi)h(g\370r)g(dette)h(v)o(ed)f(\351n)g(eller)g(\003ere) g(lister)l(,)382 1225 y(s\345)k(dette)g(har)g(tidsk)o(ompleksiteten)34 b Fu(O)s Fr(\()p Fu(n)p Fr(\))p FJ(.)28 b(Det)h(samme)f(g\346lder)i (det)f(at)f(hente)i(dataene)h(og)382 1338 y(gemme)23 b(dem)h(i)f(\002lerne.)523 1451 y(Det)k(virk)o(elige)k(sp\370r)n (gsm\345l)f(er)e(om)f(v)n(ores)j(opdelingsfunktion)j(ogs\345)c (opf\370rer)h(sig)e(line-)382 1564 y(\346rt.)d(Pseudok)o(oden)30 b(\(p\345)d(side)g(48\))f(viser)i(at)e(algoritmen)j(best\345r)e(en)g (betingelsk)o(onstrukt)q(ion)382 1677 y(hv)n(or)h(hv)o(er)f(for)n (grening)j(udg\370res)f(af)d(to)h(eller)h(tre)e(operationer)k(plus)e (et)e(kald)i(til)f(funktionen)382 1790 y(selv)20 b(med)g(et)g(element)h (mindre)f(i)g(dataene.)h(Operationerne)i(best\345r)f(af)d(tildeling)k (og)d(tilf\370jelse)382 1903 y(af)g(en)g(n)o(yt)g(element)h(til)f(en)g (liste,)g(og)g(be)o(gge)h(dele)f(er)g Fu(O)s Fr(\(1\))g FJ(\(idet)h(sidstn\346vnte)i(er)d(en)g(tilf\370jelse)382 2016 y(til)j(be)o(gyndelsen)k(af)d(listen\).)525 2129 y(O)t FH(P)t(S)t(P)t(L)t(I)t(T)t(N)t(I)t(N)t(G)37 b FJ(er)29 b(alts\345)i(en)e(rekursi)n(v)j(funktion)f(som)f(gentages)h(med)f (datam\346ngden)382 2242 y(reduceret)f(med)e(\351n)g(for)h(hv)o(er)f (iteration,)i(og)e(da)g(vi)h(kun)f(foretager)j Fu(O)s Fr(\(1\))p FJ(-operationer)h(inde)382 2355 y(i)25 b(funktionen,)j (betyder)f(dette)f(at)f(tidsk)o(ompleksiteten)31 b(for)c(O)t FH(P)t(S)t(P)t(L)t(I)t(T)t(N)t(I)5 b(N)t(G)32 b FJ(er)25 b(en)h(k)o(onstant)382 2467 y(gange)e(antallet)i(af)d(operationer)l(,)k (dvs.)d Fu(O)s Fr(\()p Fu(n)p Fr(\))p FJ(.)523 2580 y(Nuv)o(el,)f (dette)i(m\345)e(betyde)i(at)e(hele)h(v)n(ores)h(programs)g(k)o (ompleksitet)i(er)c Fu(O)s Fr(\()p Fu(n)p Fr(\))p FJ(.)382 2830 y Fw(7.5.5)99 b(K)n(onklusion)382 3004 y FJ(\305rsagen)28 b(til)g(at)f(v)n(ores)i(metode)f(er)f(langsom,)h(er)g(alts\345)g(ikk)o (e)g(algoritmen)i(i)c(sig)i(selv)g(da)f(den)382 3117 y(kan)h(udf\370res)i(i)d(o)o(v)o(erskuelig)j(tid.)e(Derfor)g(m\345)f (problemet)i(ligge)g(et)f(sted)g(i)f(implementatio-)382 3230 y(nen.)e(Sandsynligvis)j(er)d(de)g(listeoperationer)30 b(som)25 b(programmet)h(er)f(bygget)h(op)g(v)o(ed)f(hj\346lp)382 3343 y(af)h(\226)h(eftersom)h(det)f(er)f(det)h(mest)g(naturlige)i(i)d (et)g(funktionelt)k(sprog)e(som)e(SML)f(\226)h(for)h(inef-)382 3455 y(fekti)n(v)o(e)k(i)e(forhold)j(til)e(de)g(datastrukturer)k(man)29 b(ville)i(bruge)g(v)o(ed)f(en)g(implementation)j(i)c(et)382 3568 y(imperati)n(vt)c(sprog)g(som)e(C)f(eller)j(C++.)523 3681 y(Hvis)33 b(v)n(ores)i(algoritme)g(ble)n(v)e(optimeret)i(med)e (hensyn)i(til)e(hastighed,)j(s\345)d(b)n(urde)h(den)382 3794 y(som)27 b(det)i(ses,)e(ikk)o(e)i(v\346re)f(bere)o (gningsm\346ssig)j(tungere)f(end)e(de)g(andre)h(programmer)g(som)382 3907 y(vi)i(k)o(\370rer)h(i)e(testen,)i(f)o(aktisk)h(en)e(del)g (lettere)h(da)f(Lempel-Zi)n(v-algoritmerne)k(in)l(v)n(olv)o(erer)f(en) 382 4020 y(del)24 b(s\370gning)h(og)f(Burro)n(ws-Wheeler)n (-transformat)q(ion)q(en)29 b(sortering)d(som)d(er)h Fu(O)s Fr(\()p Fu(n)15 b Fr(log)h Fu(n)p Fr(\))p FJ(.)523 4133 y(Hv)n(orvidt)21 b(v)n(ores)g(algoritme)h(tilsammen)f(med)e(de)h (k)o(ompressionsalgoritmer)26 b(vi)19 b(bruger)l(,)382 4246 y(er)j(hurtigere)i(end)f(ren)f(brug)h(af)f FA(bzip2)f FJ(er)h(sv\346rere)h(at)f(sige,)g(og)g(det)h(afh\346nger)g (selvf\370lgelig)382 4359 y(af)h(m\346ngden)g(af)g(tekst)h(i)e(forhold) i(til)f(HTML)e(efter)i(opdelingen.)j(Hvis)d(der)g(f.eks.)g(kun)g(er)g (\351t)382 4472 y(te)o(gn)j(HTML)d(og)j(resten)h(er)e(tekst,)i(vil)f(v) n(ores)g(k)o(ombinerede)j(metode)d(ikk)o(e)h(v\346re)f(hurtigere)382 4585 y(end)d(ren)g(brug)g(af)f FA(bzip2)p FJ(,)f(men)h(dette)i(er)e (selvf\370lgelig)k(usandsynligt.)523 4697 y(Men)19 b(vi)h(skal)g(i)f (alt)h(bruge)g(under)h(hv)n(ad)f FA(bzip2)e FJ(bruger)j(af)e(tid,)h (alts\345)2800 4662 y Ft(1)p 2707 4677 222 4 v 2707 4730 a(14)p Fo(;)p Ft(21)p Fo(=)p Fz(s)2964 4697 y Fs(\031)25 b Fr(0)p Fu(;)p Fr(0704)g FJ(s)382 4821 y(if\370lge)h(tabel)g(7.4)f (p\345)h(side)f(54.)g(Hvis)g(fordelingen)k(bli)n(v)o(er)d(50\045)f(til) g(hv)o(er)g(del,)h(vil)f(dette)h(alts\345)382 4933 y(sige)32 b(at)f(vi)g(har)h Fr(0)p Fu(;)p Fr(0704)25 b FJ(s)h Fs(\000)g Fr(\()1381 4898 y Ft(1)p 1381 4913 36 4 v 1381 4965 a(2)1453 4933 y Fs(\001)1607 4898 y Ft(1)p 1514 4913 222 4 v 1514 4966 a(65)p Fo(;)p Ft(22)p Fo(=)p Fz(s)1772 4933 y Fr(+)1878 4898 y Ft(1)p 1878 4913 36 4 v 1878 4965 a(2)1949 4933 y Fs(\001)h Fr(0)p Fu(;)p Fr(0704)e FJ(s)p Fr(\))40 b(=)g(0)p Fu(;)p Fr(0275)25 b FJ(s)31 b(til)g(opdelingen.)382 5046 y(Dette)23 b(sv)n(arer)h(til)g(at)f(v)n(ores)h(opsplitter)i(skal)e (kunne)h(tage)f(36,33)g(\002ler)e(pr)-5 b(.)23 b(sek,)h(eller)g (omkring)382 5159 y(halvdelen)j(af)e(hv)n(ad)h FA(gzip)d FJ(viste)j(sig)f(at)f(kunne)j(klare.)e(S\345)f(v)o(ed)h(denne)h (fordeling)i(synes)e(det)382 5272 y(rimeligt)f(at)e(dette)h(kan)g(lade) h(sig)e(g\370re.)1831 5652 y(56)p eop %%Page: 57 59 57 58 bop 382 1171 a FC(Kapitel)43 b(8)382 1586 y FK(Praktisk)n(e)52 b(o)n(v)n(er)n(v)n(ejelser)382 2031 y FJ(I)19 b(dette)i(kapitel)h (g\370r)e(vi)g(os)g(nogle)h(o)o(v)o(erv)o(ejelser)h(om)e(den)g (praktisk)o(e)j(an)l(v)o(endelighed)h(af)c(v)n(ores)382 2144 y(resultater)26 b(\226)d(er)g(der)h(o)o(v)o(erho)o(v)o(edet)i (nogen)f(der)f(vil)f(bruge)i(k)o(ompression)i(af)c(HTML-sider?)523 2257 y(Det)35 b(viser)h(sig)g(at)f(det)h(er)f(der)l(,)g(for)h(der)g (\002ndes)f(f)o(aktisk)i(allerede)h(l\370sninger)g(p\345)d(mar)n(-)382 2369 y(k)o(edet,)f(HTTP)d(1.1-standarden)37 b(indeholder)f(bl.a.)d(et)g (afsnit)i(om)d(emnet)i(\(mere)f(om)g(det)g(i)382 2482 y(afsnit)28 b(8.3\).)f(Men)g(det)h(er)f(langt)h(fra)f(alle)h(der)f(udn) o(ytter)i(muligheden)h(for)d(k)o(ompression,)j(se)382 2595 y(f.eks.)25 b(en)g(mindre)g(unders\370gelse)k(af)c(udbredelse)i (af)e(HTTP)d(1.1-k)o(ompression)29 b(i)24 b(Danmark)382 2708 y(i)g(appendiks)k(D)c(p\345)h(side)g(75)g(\226)g(det)g(viser)h (sig)f(at)g(ingen)h(af)e(de)h(20)g(st\370rste)i(steder)f(i)e(Danmark) 382 2821 y(ben)o(ytter)h(k)o(ompression.)h(Hv)n(orfor)f(bli)n(v)o(er)f (det)g(ikk)o(e)g(brugt)h(noget)g(mere?)523 2934 y(F)o(or)32 b(at)h(klarl\346gge)i(dette)f(sp\370r)n(gsm\345l)i(gennemg\345r)f(vi)e (f\370rst)h(fordele)h(og)e(ulemper)i(for)382 3047 y(HTML-k)o (ompression)27 b(generelt,)f(b\345de)g(for)g(bruger)g(og)f(for)h (udbyder)l(,)h(dern\346st)f(for)f(de)g(spe-)382 3160 y(ci\002kk)o(e)f(fordele)h(og)f(ulemper)h(v)o(ed)e(brug)i(af)e (muligheden)j(i)d(HTTP)e(1.1-standarden.)382 3452 y FB(8.1)119 b(F)m(ordele)31 b(og)e(ulemper)i(f)m(or)e(udbyder)382 3659 y FJ(Udbyderne)d(vil)f(naturligvis)j(kun)d(bruge)g(l\370sningen)i (hvis)f(det)e(kan)h(betale)h(sig)f(\370k)o(onomisk.)382 3772 y(Det)h(kan)g(det)h(hvis)g(udbyderen)i(kan)d(spare)i(penge)f(v)o (ed)g(at)f(indf\370re)h(HTML-k)o(ompression)h(i)382 3885 y(stedet)d(for)e(en)h(internetforbindelse)29 b(med)24 b(st\370rre)g(b\345ndbredde.)523 3998 y(Det)h(kan)h(dog)g(v\346re)g(at) f(de)h(skal)g(ans\346tte)g(en)g(teknik)o(er)i(for)d(at)h(installere)i (l\370sningen,)g(og)382 4111 y(dette)j(k)o(oster)g(ekstra)g(penge.)g (Det)e(kan)i(ogs\345)f(vise)h(sig)f(at)g(k)o(ompression)i(af)e(HTML)e (s\346tter)382 4224 y(s\345)j(store)h(bere)o(gningsm\346ssige)j(kra)n (v)d(til)f(udbyderens)j(maskinpark)f(at)e(udgifterne)j(til)d(n)o(ye)382 4337 y(computere)25 b(bli)n(v)o(er)g(st\370rre)f(end)g(udgifterne)j (til)c(en)h(n)o(y)f(forbindelse.)523 4450 y(En)28 b(st\370rre)h (forbindelse)j(k)o(oster)d(dog)g(\003ere)f(penge)i(hv)o(ert)f(kv)n (artal,)g(mens)g(prisen)g(for)g(en)382 4563 y(systemopgraderin)i (afh\346nger)e(af)e(hv)n(or)h(hurtigt)g(hardw)o(aren)h(bli)n(v)o(er)f (for\346ldet.)g(S\345)e(rentabi-)382 4676 y(liteten)f(afh\346nger)g(af) e(sk\346ringspunktet)28 b(mellem)23 b(de)h(to.)523 4789 y(V)-12 b(ores)21 b(hastighedstest)j(har)c(vist)h(at)f(det)g(er)g (muligt)g(at)g(k)o(omprimere)i(65)e(sider)h(pr)-5 b(.)19 b(sekund,)382 4901 y(mens)33 b(f.eks.)h Fv(jubii.dk)29 b FJ(har)k(omkring)i(26)f(mill.)e(side)n(visninger)38 b(pr)-5 b(.)33 b(uge)g(\(for)h(uge)g(48,)382 5014 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b(en)g(hel)h(del)f(h\370jere)i(end)e(den)h(gennemsnitlige\),)j(men)c (det)g(ses)h(at)f(ydelsen)i(er)e(inden)382 774 y(for)37 b(r\346kk)o(e)n(vidde,)h(selv)f(v)o(ed)g(Jubii)g(som)g(le)n(v)o(erer)g (langt)h(\003est)e(sider)h(i)f(Danmark)h(pr)-5 b(.)37 b(uge.)382 887 y(Priseksemplet)31 b(for)e(Cybercity)i(Erhv)o(erv)e(i)f (tabel)i(3.4)f(p\345)g(side)g(15)g(viser)h(at)e(anskaf)n(felse)k(af)382 1000 y(f.eks.)25 b(en)h(enk)o(elt)h(serv)o(er)f(sagtens)h(ville)g (kunne)f(tjenes)h(ind)f(p\345)f(en)h(besparelse)i(med)d(hensyn)382 1112 y(til)e(linjen.)523 1225 y(Endeligt)42 b(kr\346v)o(er)e (l\370sningen)k(i)c(\370)o(vrigt)h(at)f(brugerne)j(kan)e(dek)o (omprimere)i(HTML-)382 1338 y(\002lerne,)25 b(og)f(udbyderen)k(skal)d (v\346re)g(sikk)o(er)h(p\345)e(at)g(dette)i(er)e(tilf\346ldet)i(for)f (at)f(undg\345)i(at)f(miste)382 1451 y(bes\370gende.)382 1744 y FB(8.2)119 b(Bruger)n(ne)382 1951 y FJ(F)o(or)18 b(at)h(f\345)g(brugerne)i(til)e(at)g(acceptere)i(k)o(ompression)h(skal) d(de)g(moti)n(v)o(eres)i(v)o(ed)e(enten)h(at)f(kunne)382 2064 y(ople)n(v)o(e)28 b(en)e(hastighedsm\346ssig)31 b(ge)n(vinst)d(v)o(ed)f(brugen)h(eller)g(simpelthen)h(ikk)o(e)e(at)g (kunne)h(se)382 2177 y(visse)c(sider)-5 b(.)25 b(Eller)e(e)n(vt.)g (blot)i(ikk)o(e)f(opdage)h(at)f(det)f(sk)o(er)-5 b(.)523 2290 y(K)m(ompression)27 b(af)f(HTML)d(nedbringer)28 b(tra\002kk)o(en)f(til)e(udbyderen)k(s\345)c(brugeren)j(vil)e(op-)382 2402 y(le)n(v)o(e)d(at)f(det)h(g\345r)g(hurtigere)i(at)d(hente)i(siden) g(ned.)f(V)-5 b(i)21 b(har)i(udf\370rt)h(en)f(test,)f(se)h(tabel)g(8.1) g(\(selv)o(e)382 2515 y(unders\370gelsen)k(er)d(dokumenteret)i(i)d (appendiks)j(B.3)c(p\345)h(side)h(72\),)g(som)f(viser)h(at)f(tiden)h (kan)382 2628 y(nedbringes)30 b(v\346sentligt)g(v)o(ed)e(at)f(hente)h (HTML-\002lerne)f(k)o(omprimeret,)i(ogs\345)g(selv)f(om)f(der)382 2741 y(allerede)f(bruges)g(k)o(ompression)h(p\345)d(den)h(forbindelse)i (man)d(bruger)-5 b(.)25 b(Is\346r)f(for)h(modem)f(hv)n(or)382 2854 y(vi)i(f.eks.)h(har)f(reduceret)j(tiden)f(for)e(Jyllandspostens)32 b(side)27 b(fra)f(15,3)h(sekunder)i(til)d(3,41)h(se-)382 2967 y(kunder)-5 b(.)30 b(Denne)f(tid)g(er)g(dog)g(uden)g(tiden)h(for)f (k)o(ompression/dek)o(ompre)q(ssi)q(on)q(,)k(men)c(denne)382 3080 y(vil)19 b(v\346re)h(lille)g(pga.)f(af)g(\002lernes)h (st\370rrelse,)i(se)d(e)n(vt.)g(hv)n(or)h(mange)g(\002ler)f(man)g(kan)h (k)o(omprimere)382 3193 y(pr)-5 b(.)23 b(sekund)i(i)e(tabel)i(7.4)e (p\345)h(side)g(54.)p 618 3319 2516 8 v 668 3424 a(HTML-side)201 b(modem)24 b(\(s\))100 b(ISDN)22 b(\(s\))101 b(ADSL)21 b(\(s\))100 b(\002lst\370r)-5 b(.)24 b(\(kb\))p 618 3478 2516 5 v 668 3582 a(Carlsber)n(g)402 b(0,47)303 b(0,05)285 b(0,06)344 b(2,5)668 3695 y(The)23 b(V)-12 b(oice)383 b(1,14)303 b(0,12)285 b(0,14)344 b(4,7)668 3808 y(IT)-8 b(-A)h(visen)394 b(1,23)303 b(0,12)285 b(0,13)344 b(4,6)668 3921 y(ITL)609 b(0,96)303 b(0,10)285 b(0,12)344 b(4,2)668 4034 y(Jyllandsposten)221 b(3,41)303 b(0,48)285 b(0,41)322 b(12,0)668 4147 y(Jubii)576 b(2,24)303 b(0,24)285 b(0,25)344 b(7,7)p 618 4204 2516 8 v 727 4382 a FD(T)-8 b(abel)23 b(8.1:)31 b(Overf\370r)o(selstiderne)e(for)24 b(de)f(k)o(omprimer)m (ede)j(HTML-\002ler)523 4594 y FJ(Man)32 b(kunne)h(mene)f(at)g (reduktionerne)k(for)c(de)g(hurtigere)i(forbindelser)i(er)c(s\345)f (sm\345)h(at)382 4706 y(de)25 b(er)f(uden)i(betydning,)h(men)e(f)o (aktisk)i(skal)e(sv)n(artiderne)j(i)c(programmer)i(generelt)h(v\346re)e (p\345)382 4819 y(under)g(0,2)e(sekunder)j(for)e(at)f(de)h(virk)o(er)g (som)g(om)f(de)g(reagerer)j(\003ydende)e([2)q(].)523 4932 y(Problemet)g(med)e(at)h(brugerne)i(skal)e(kunne)h(dek)o (omprimere)i(HTML-\002lerne)c(kan)h(l\370ses)382 5045 y(v)o(ed)30 b(f.eks.)g(et)g(plugin)i(til)e(en)g(bro)n(wser)h(\226)f (dette)h(gi)n(v)o(er)g(en)f(n\346sten)h(transparent)i(l\370sning)f(da) 382 5158 y(plugin)26 b(automatisk)g(kan)f(installeres)i(og)d (s\345ledes)i(ikk)o(e)f(kr\346v)o(er)g(me)o(get)f(viden)i(af)e (brugeren.)382 5271 y(Under)k(alle)h(omst\346ndigheder)j(skal)c(det)h (v\346re)f(me)o(get)g(let)h(at)f(installere)i(l\370sningen)h(\226)d (man)382 5384 y(kan)c(n\346ppe)g(forv)o(ente)h(me)o(get)f(mere)f(end)h (et)g(klik)g(p\345)f(\204OK\223)g(af)g(den)h(j\346vne)g(bruger)-5 b(.)1831 5652 y(58)p eop %%Page: 59 61 59 60 bop 1284 228 a FI(Kapitel)25 b(8:)e(Praktisk)o(e)i(o)o(v)o(erv)o (ejelser)p 382 266 2989 4 v 523 548 a FJ(Selv)o(e)30 b(udf\370rselstiden)35 b(for)c(dek)o(omprimeringen)j(betyder)e(ikk)o(e) f(noget)h(da)e(den)h(for)g(de)382 661 y(unders\370gte)22 b(algoritmer)f(er)d(s\345)h(k)o(ort)h(at)e(det)h(ikk)o(e)h(kan)f (m\346rk)o(es)g(med)g(en)g(almindelig)i(st\370rrelse)382 774 y(HTML-side.)382 1066 y FB(8.3)119 b(Eksister)n(ende)30 b(l\370sninger)382 1273 y FJ(Med)c(HTTP)d(1.1)i([7)q(])g(ble)n(v)i(der) f(indf\370rt)h(en)f(mulighed)h(for)f(k)o(ompression)j(mellem)d(webser)n (-)382 1386 y(v)o(ere)32 b(og)g(bro)n(wsere.)g(Standarden)i(ble)n(v)e (f\346rdig)h(i)e(juni)h(1999,)g(og)g(stort)h(set)f(alle)g(bro)n(wsere) 382 1499 y(og)g(HTTP-serv)o(ere)f(siden)i(den)g(dato)f(underst\370tter) j(den)e([11)q(])e(og)h(de)g(k)o(omprimeringsme-)382 1612 y(toder)g(den)g(de\002nerer:)g FA(gzip)p FJ(,)d FA(compress)g FJ(og)i FA(deflate)p FJ(,)e(alle)j(baseret)g(p\345)f(Lempel-Zi)n(v-)382 1725 y(algoritmerne.)523 1838 y(Idet)e(webserv)o(er)g(og)f(bro)n(wser)h (nu)f(har)h(en)f(standard)i(at)e(kn)o(ytte)h(sig)f(til)g(n\345r)h(de)f (skal)h(ud-)382 1951 y(v)o(eksle)21 b(k)o(omprimeret)i(data,)e(er)f (det)h(ble)n(v)o(et)g(nemt)f(at)g(k)o(omprimere)j(HTML.)17 b(K)m(ompressions-)382 2064 y(l\370sninger)32 b(\002ndes)e(til)f(de)h (to)f(mest)g(brugte)i(webserv)o(ere,)g(Microsoft)g(Internet)g (Information)382 2177 y(Serv)o(er)22 b(\(IIS\))g(og)g(Apache,)h(som)f (udg\370r)h(t\346t)f(p\345)g(90\045)g(af)g(samtlige)i(webserv)o(ere)g (p\345)e(internet-)382 2290 y(tet)i([12)q(].)523 2402 y(Da)34 b(b\345de)h(serv)o(ere)h(og)e(bro)n(wsere)i(underst\370tter)i 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h(s\345)f(de)g(skal)h(blot)382 4709 y(installere)e(et)e(modul)g(til)g (webserv)o(eren.)h(Bere)o(gningskraft)i(er)d(desuden)i(blot)e(et)g (sp\370r)n(gsm\345l)382 4822 y(om)21 b(penge,)i(s\345)f(et)f(direkte)j (problem)f(ligger)g(heller)g(ikk)o(e)f(i)g(arbejdsmidlerne,)j(blot)e (kan)f(disse)382 4934 y(v\346re)h(for)h(dyre.)523 5047 y(Or)n(ganisatorisk)g(kan)d(der)g(v\346re)g(et)g(k)o (ommunikationsproblem)26 b(hvis)21 b(ledelsen)i(er)e(d\345rlig)382 5160 y(til)27 b(at)h(f\370lge)g(arbejdsprocessen.)33 b(Der)27 b(er)g(m\345sk)o(e)i(ble)n(v)o(et)f(ansat)h(for)e(f\345)h (folk)g(og)g(de)f(ikk)o(e)i(har)382 5273 y(tid)24 b(til)f(at)h (unders\370ge)i(l\370sningerne,)h(og)c(dermed)i(ikk)o(e)f(v)o(ed)g(at)f (de)g(eksisterer)-5 b(.)1831 5652 y(59)p eop %%Page: 60 62 60 61 bop 1284 228 a FI(Kapitel)25 b(8:)e(Praktisk)o(e)i(o)o(v)o(erv)o (ejelser)p 382 266 2989 4 v 523 548 a FJ(Produktm\346ssigt)37 b(mener)e(vi)f(heller)i(ikk)o(e)f(at)g(der)g(er)f(et)h(problem)g(da)g (k)o(ompression)i(i)382 661 y(HTTP)22 b(1.1)j(kan)g(fore)o(g\345)h(med) f(en)f(anerk)o(endt)k(og)d(udbredt)i(standard,)g(nemlig)e FA(gzip)e FJ(som)i(vi)382 774 y(f)o(aktisk)g(ar)n(gumenterede)i(for)d (brugen)h(af)f(i)f(afsnit)h(6.4)g(p\345)f(side)i(46.)523 887 y(Det)31 b(kan)g(dog)h(v\346re)e(at)h(udbyderne)j(enten)e(ikk)o(e)g (v)o(ed)f(at)g(de)g(kan)h(spare)g(penge)g(v)o(ed)f(at)382 1000 y(k)o(omprimere)e(deres)g(sider)l(,)g(eller)g(som)e (f\370rn\346vnt,)i(at)f(der)g(o)o(v)o(erho)o(v)o(edet)i(eksisterer)g (en)e(l\370s-)382 1112 y(ning.)j(Alts\345)g(direkte)h(eller)f (indirekte)i(et)d(vidensm\346ssigt)j(problem)f(\226)e(ideen)i(om)d(at)i (k)o(om-)382 1225 y(primere)h(HTML)d(og)j(HTTP)c(1.1')-5 b(s)32 b(underst\370ttelse)k(af)31 b(det)h(synes)g(at)f(v\346re)h(en)f (v)o(elbe)n(v)n(aret)382 1338 y(hemmelighed.)f(Yderligere)f(kan)f(det)h (v\346re)e(at)h(udbyderne)j(tror)d(at)f(den)i(st\370rste)g(del)f(af)g (de-)382 1451 y(res)i(tra\002k)f(er)g(billeder)j(og)d(lyd,)h(og)f (dermed)i(ikk)o(e)f(tror)g(at)f(HTML-k)o(ompression)i(vil)f(v\346re)382 1564 y(\370k)o(onomisk)g(gunstigt,)g(selv)n(om)f(vi)f(tidligere)i(i)e (rapporten)i(har)f(vist)f(at)g(dette)h(ikk)o(e)g(beh\370)o(v)o(er)382 1677 y(at)23 b(v\346re)h(tilf\346ldet.)523 1790 y(V)-5 b(i)17 b(har)h(p\345)h(bagrund)h(af)e(denne)i(hypotese)g(spur)n(gt)g (udbydere)h(af)d(nogle)h(f\345)f(udv)n(algte)j(st\370rre)382 1903 y(websites)38 b(om)d(hv)n(orfor)k(de)d(ikk)o(e)h(bruger)h(k)o (ompression)h(\(unders\370gelsen)i(er)36 b(beskre)n(v)o(et)i(i)382 2016 y(appendiks)29 b(E)24 b(p\345)i(side)h(76\).)f(Ud)f(af)h(de)g(tre) g(adspur)n(gte)j(udbydere)f(v)n(ar)e(der)h(kun)f(\351n)g(som)g(ga)n(v) 382 2129 y(indtryk)f(af)e(at)f(ha)n(v)o(e)i(unders\370gt)i(muligheden)f (n\370jere.)f(V)-5 b(i)22 b(tolk)o(er)i(sv)n(arene)h(s\345ledes)g(at)e (denne)382 2242 y(f)o(aktisk)i(ha)n(vde)f(unders\370gt)i(potentialet)g (n\346rmere)e(og)f(foretaget)i(en)e(test,)g(mens)h(de)f(to)g(andre)382 2355 y(v)n(ar)g(helt)i(eller)f(delvist)h(uvidende)h(om)d(muligheden.) 523 2467 y(Med)37 b(mere)f(viden)i(b)n(urde)g(der)f(v\346re)g(en)f (stor)i(chance)g(for)f(at)f(udbyderne)k(vil)d(bruge)382 2580 y(k)o(ompression)h(af)d(HTML)e(n\345r)j(det)g(er)f(del)h(af)f(en)g (allerede)i(accepteret)h(standard,)g(v)o(ed)d(at)382 2693 y(s\346tte)26 b(et)h(kryds)g(i)f(et)h(indstillingsvindue)32 b(i)26 b(Microsofts)i(IIS)e(eller)h(installerede)j FA(mod_gzip)382 2806 y FJ(til)20 b(Apache.)h(Eftersom)g(alle)f(n)o(yere)h(bro)n(wsere)h (underst\370tter)h(standarden,)g(er)d(det)h(i)e(hv)o(ert)i(f)o(ald)382 2919 y(klart)j(at)g(initiati)n(v)o(et)h(ligger)g(hos)f(udbyderne.)523 3032 y(Med)g(mere)f(viden)i(hviler)g(an)l(v)o(endelsen)i(af)d(k)o (ompression)i(af)e(HTML)d(udelukk)o(ende)28 b(p\345)382 3145 y(at)e(en)g(e)n(vt.)f(in)l(v)o(estering)k(i)d(re)o(gnekraft)i(er)e (billigere)i(end)e(at)g(in)l(v)o(estere)i(i)e(ekstra)h(b\345ndbredde.) 382 3258 y(En)20 b(s\345dan)i(analyse)g(afh\346nger)g(naturligvis)i(af) c(b\345de)i(af)e(tid)h(og)g(sted)g(og)g(m\345)f(derfor)i(foretages)382 3371 y(v)o(ed)i(den)g(enk)o(elte)h(udbyder)-5 b(.)1831 5652 y(60)p eop %%Page: 61 63 61 62 bop 382 1171 a FC(Kapitel)43 b(9)382 1586 y FK(K)-5 b(onklusion)382 2067 y FB(9.1)119 b(Resultater)30 b(fra)f(rapporten)382 2274 y FJ(Efter)24 b(den)g(k)o(orte)h(introduktion)j(til)23 b(k)o(ompression)k(har)d(vi)g(foretaget)i(en)e(analyse)i(af)e(beho)o(v) o(et)382 2387 y(for)19 b(k)o(ompression)i(af)d(HTML-sider)-5 b(.)18 b(Den)g(viser)i(at)e(der)h(for)g(brugerne)h(kan)f(v\346re)g(en)f (ge)n(vinst)i(i)382 2500 y(form)f(af)f(en)h(tidsbesparelse)k(\226)c (alts\345)g(en)g(ople)n(v)o(else)i(af)e(et)f(hurtigere)k(internet.)e(F) o(or)e(udbyderne)382 2613 y(af)29 b(siderne)j(kan)e(der)g(v\346re)f(en) h(betydelig)i(\370k)o(onomisk)g(ge)n(vinst)f(hvis)f(k)o(omprimeringen)j (er)382 2726 y(ef)n(fekti)n(v)25 b(nok,)g(b\345de)g(med)f(hensyn)i(til) e(at)g(mindsk)o(e)h(st\370rrelsen)i(af)d(store)h(og)f(sm\345)g(sider)l (,)h(men)382 2839 y(ogs\345)f(med)g(hensyn)h(til)e(hastighed.)523 2952 y(F)o(or)i(at)g(f\345)g(et)h(grundlag)h(for)f(forst\345else)i(af)d (hv)n(or)i(me)o(get)e(og)h(hv)n(orfor)i(HTML)23 b(kan)j(k)o(om-)382 3065 y(primeres,)35 b(har)f(vi)g(unders\370gt)i(emnet)f (informationsteori,)j(og)c(vi)g(kan)g(k)o(onstatere)j(at)c(den)382 3178 y(m\346ngde)23 b(data)h(man)f(skal)h(bruge)g(til)f(at)g (repr\346sentere)j(et)d(te)o(gn)g(med,)g(er)g(indenfor)i FD(entr)l(opien)382 3290 y FJ(af)18 b(dataene)i(plus)f(\351n.)f(V)-5 b(i)17 b(har)i(ogs\345)g(k)o(onstateret)i(at)d(entropien)j(kan)e (reduceres)i(yderligere)g(v)o(ed)382 3403 y(at)e(tage)h(st\370rre)h (blokk)o(e)g(af)e(te)o(gn)h(i)f(betragtning,)j(hvis)e(der)g(i)f (dataene)i(fore\002ndes)g(afh\346ngighe-)382 3516 y(der)h(imellem)f(de) h(enk)o(elte)h(te)o(gn.)e(Da)g(vi)g(desuden)j(har)e(k)o(onstateret)i (at)d(der)h(er)f(afh\346ngigheder)382 3629 y(og)j(redundans)i(i)d (HTML,)e(kan)j(vi)f(k)o(onkludere)k(at)d(HTML)d(kan)j(k)o(omprimeres.) 523 3742 y(P\345)e(denne)h(baggrund)i(har)e(vi)f(unders\370gt)k(forsk)o (ellige)f(algoritmer)g(for)d(at)g(klarl\346gge)j(de-)382 3855 y(res)18 b(styrk)o(er)i(og)e(sv)n(agheder)j(i)d(forbindelse)j(med) d(k)o(ompression)j(af)d(HTML.)e(V)-5 b(i)17 b(har)h(unders\370gt)382 3968 y(en)i(algoritme,)h(Huf)n(fman-k)o(odning,)h(der)e(kan)g(bruges)i (til)d(at)h(k)o(ode)g(dataene)i(s\345)d(st\370rrelsen)k(n\345r)382 4081 y(ned)h(i)f(det)h(optimale)h(omr\345de.)523 4194 y(V)-5 b(i)26 b(unders\370gt)k(ordbogsbaserede)j(algoritmer)d(og)d(har) h(fundet)h(ud)f(af)f(at)g(de)h(udm\346rk)o(er)382 4307 y(sig)j(v)o(ed)f(k)o(ompression)k(af)c(ens)h(blokk)o(e)h(best\345ende)h (af)e(\003ere)f(te)o(gn,)h FD(m\370nstr)m(e)p FJ(,)g(og)f(derfor)i(er) 382 4420 y(gode)c(til)f(HTML-tags.)g(Derudo)o(v)o(er)h(kan)g(de)f(med)g (fordel)i(k)o(ombineres)g(med)e(Huf)n(fman)h(s\345-)382 4532 y(dan)g(at)f(styrk)o(erne)j(v)o(ed)d(de)h(to)f(principper)j (forenes.)f(LZ77)e(er)g(en)g(af)g(disse)i(algoritmer)g(og)e(i)382 4645 y(k)o(ombination)f(med)e(Huf)n(fman)f(implementeret)j(i)d(det)h (udbredte)i(program)f FA(gzip)p FJ(.)523 4758 y(Derudo)o(v)o(er)19 b(har)g(vi)f(unders\370gt)i(en)f(transformation,)i(Burro)n(ws-wheeler)n (-transformatio)q(ne)q(n,)382 4871 y(der)f(efterfulgt)j(af)d(et)f (princip)j(v)o(ed)e(na)n(vn)h(mo)o(v)o(e-to-front)i(kan)d(resultere)j (i)c(data)i(der)f(kan)h(k)o(om-)382 4984 y(primeres)j(me)o(get)g(ef)n (fekti)n(vt)h(med)d(Huf)n(fman-k)o(odning.)27 b(De)22 b(tre)i(algoritmer)h(er)e(k)o(ombineret)i(i)382 5097 y(programmet)g FA(bzip2)p FJ(.)523 5210 y(Efter)30 b(unders\370gelse)35 b(af)30 b(de)h(forsk)o(ellige)i(k)o(ompressionsalgorit)q(mer)j(har)31 b(vi)f(beskre)n(v)o(et)382 5323 y(tre)k(mulige)h(l\370sninger)i(som)d (kunne)h(t\346nk)o(e)g(sig)f(at)g(v\346re)h(brugbare.)h(Ud)d(af)h (disse)h(har)g(vi)1831 5652 y(61)p eop %%Page: 62 64 62 63 bop 1474 228 a FI(Kapitel)24 b(9:)g(K)m(onklusion)p 382 266 2989 4 v 382 548 a FJ(v)n(algt)j(at)f(implementere)j(den)e (sidste,)g(nemlig)g(opdeling)i(af)d(HTML-\002len)f(i)h(tre,)g(tags,)h (tekst)382 661 y(og)g(en)f(k)o(ontrol\002l,)j(for)d(at)h(se)g(om)f(det) h(kan)g(betale)h(sig)f(at)f(k)o(omprimere)j(de)d(forsk)o(ellige)k(dele) 382 774 y(af)d(\002len)g(hv)o(er)h(for)f(sig.)h(P\345)e(baggrund)k(af)d (v)n(ores)i(unders\370gelse)i(af)c(algoritmer)i(har)f(vi)f(v)n(algt)382 887 y(at)g(bruge)h FA(gzip)d FJ(p\345)i(HTML-delen)g(og)g FA(bzip2)f FJ(p\345)h(tekstdelen.)i(K)m(ontrol\002len)g(best\345r)f(af) f(en)382 1000 y(r\346kk)o(e)d(tal)g(som)f(vi)g(k)o(omprimerer)j(med)d (Huf)n(fman-k)o(odning.)523 1112 y(Efter)31 b(implementering)k(af)c(v)n (ores)i(l\370sning)g(har)f(vi)f(fundet)i(ud)e(af)g(at)h(v)n(ores)g (algoritme)382 1225 y(ikk)o(e)i(k)o(omprimerer)h(bedre)f(end)f (eksisterende)k(l\370sninger)-5 b(.)35 b(Man)e(kan)g(dog)h(muligvis)g (l\370se)382 1338 y(dette)j(problem)h(v)o(ed)f(at)f(sk\346re)h (taldelen)h(fra,)f(for)f(i)g(stedet)i(at)e(mark)o(ere)i(o)o(v)o(er)n (gangen)h(fra)382 1451 y(HTML)27 b(til)i(tekst)h(med)f(et)g(\003ag.)g (Desv\346rre)h(vidste)g(det)g(sig)f(at)g(v)n(ores)i(implementering)h(v) n(ar)382 1564 y(me)o(get)j(langsom,)g(v)o(ed)g(at)g(unders\370ge)i(v)n (ores)f(implementering)i(med)c(teoretisk)j(tidsk)o(om-)382 1677 y(pleksitet)26 b(f)o(andt)e(vi)g(ud)f(af)h(at)f(problemet)j(sk)o (yldtes)f(implementeringen)i(af)d(splitteren.)523 1790 y(F)o(or)g(at)h(\002nde)g(ud)g(af)f(om)g(v)n(ores)j(l\370sning)f(vil)f (bli)n(v)o(e)h(brugt)g(har)f(vi)g(gjort)g(os)g(nogle)h(prakti-)382 1903 y(sk)o(e)c(o)o(v)o(erv)o(ejelser)l(,)j(hv)n(or)e(vi)e(har)i (fundet)g(ud)f(af)g(at)f(med)h(mere)g(viden)h(b)n(urde)g(der)g(v\346re) e(en)h(stor)382 2016 y(chance)i(for)f(at)f(udbyderne)j(vil)e(bruge)h (HTML-k)o(omprimering.)f(Specielt)h(n\345r)f(det)g(er)f(en)h(del)382 2129 y(af)f(en)h(allerede)i(accepteret)g(standard)g(som)e(HTTP)d(1.1)i (som)h(fjerner)h(de)f(\003este)g(ulemper)h(ud-)382 2242 y(byderne)j(og)e(brugerne)j(kan)e(k)o(omme)f(ud)g(for)-5 b(.)25 b(Det)g(eneste)i(tilbage)n(v\346rende)h(problem)f(er)e(de)382 2355 y(in)l(v)o(esteringer)33 b(i)c(bere)o(gningskraft)34 b(som)29 b(udbyderne)j(muligvis)f(skal)f(foretage.)h(Det)e(virk)o(er) 382 2467 y(dog)20 b(som)g(om)f(det)i(ville)g(v\346re)e(v\346sentligt)j (billigere)h(end)d(at)g(in)l(v)o(estere)i(i)e(ekstra)h(b\345ndbredde.) 382 2760 y FB(9.2)119 b(P)n(erspekti)o(v)o(ering)382 2967 y FJ(Der)28 b(er)g(for)h(os)g(ingen)h(tvi)n(vl)f(om)f(at)g(k)o (omprimering)j(af)e(HTML)d(pt.)i(er)h(en)f(god)h(id\351.)g(Der)f(er)382 3080 y(penge)d(at)e(spare)i(for)e(udbyderne)k(og)c(siderne)j(vil)d (indl\346ses)i(hurtigere)h(for)e(brugerne.)523 3193 y(Man)e(kan)g (naturligvis)k(ar)n(gumentere)e(for)f(at)f(man)f(i)h(takt)g(med)g (udviklingen)k(kan)c(f\345)g(hur)n(-)382 3306 y(tigere)i (internetforbindelse)q(r)k(til)23 b(den)g(samme)g(pris.)g(Men)f(det)i (samme)e(g\346lder)i(processorer)l(,)382 3419 y(og)h(rentabiliteten)k (i)24 b(HTML-k)o(ompression)j(afh\346nger)f(derfor)h(af)d(udviklingen) 29 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