%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: auszug.dvi %%Pages: 15 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips auszug %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2002.01.24:1537 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 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M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: pstricks.pro %! % PostScript prologue for pstricks.tex. % Version 97 patch 3, 98/06/01 % For distribution, see pstricks.tex. % /tx@Dict 200 dict def tx@Dict begin /ADict 25 dict def /CM { matrix currentmatrix } bind def /SLW /setlinewidth load def /CLW /currentlinewidth load def /CP /currentpoint load def /ED { exch def } bind def /L /lineto load def /T /translate load def /TMatrix { } def /RAngle { 0 } def /Atan { /atan load stopped { pop pop 0 } if } def /Div { dup 0 eq { pop } { div } ifelse } def /NET { neg exch neg exch T } def /Pyth { dup mul exch dup mul add sqrt } def /PtoC { 2 copy cos mul 3 1 roll sin mul } def /PathLength@ { /z z y y1 sub x x1 sub Pyth add def /y1 y def /x1 x def } def /PathLength { flattenpath /z 0 def { /y1 ED /x1 ED /y2 y1 def /x2 x1 def } { /y ED /x ED PathLength@ } {} { /y y2 def /x x2 def PathLength@ } /pathforall load stopped { pop pop pop pop } if z } def /STP { .996264 dup scale } def /STV { SDict begin normalscale end STP } def /DashLine { dup 0 gt { /a .5 def PathLength exch div } { pop /a 1 def PathLength } ifelse /b ED /x ED /y ED /z y x add def b a .5 sub 2 mul y mul sub z Div round z mul a .5 sub 2 mul y mul add b exch Div dup y mul /y ED x mul /x ED x 0 gt y 0 gt and { [ y x ] 1 a sub y mul } { [ 1 0 ] 0 } ifelse setdash stroke } def /DotLine { /b PathLength def /a ED /z ED /y CLW def /z y z add def a 0 gt { /b b a div def } { a 0 eq { /b b y sub def } { a -3 eq { /b b y add def } if } ifelse } ifelse [ 0 b b z Div round Div dup 0 le { pop 1 } if ] a 0 gt { 0 } { y 2 div a -2 gt { neg } if } ifelse setdash 1 setlinecap stroke } def /LineFill { gsave abs CLW add /a ED a 0 dtransform round exch round exch 2 copy idtransform exch Atan rotate idtransform pop /a ED .25 .25 % DG/SR modification begin - Dec. 12, 1997 - Patch 2 %itransform translate pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a itransform pathbbox /y2 ED a Div ceiling cvi /x2 ED /y1 ED a % DG/SR modification end Div cvi /x1 ED /y2 y2 y1 sub def clip newpath 2 setlinecap systemdict /setstrokeadjust known { true setstrokeadjust } if x2 x1 sub 1 add { x1 % DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) % a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore } % def a mul y1 moveto 0 y2 rlineto stroke /x1 x1 1 add def } repeat grestore pop pop } def % DG/SR modification end /BeginArrow { ADict begin /@mtrx CM def gsave 2 copy T 2 index sub neg exch 3 index sub exch Atan rotate newpath } def /EndArrow { @mtrx setmatrix CP grestore end } def /Arrow { CLW mul add dup 2 div /w ED mul dup /h ED mul /a ED { 0 h T 1 -1 scale } if w neg h moveto 0 0 L w h L w neg a neg rlineto gsave fill grestore } def /Tbar { CLW mul add /z ED z -2 div CLW 2 div moveto z 0 rlineto stroke 0 CLW moveto } def /Bracket { 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sub def n { Lineto } repeat CP 4 2 roll ArrowB L pop pop } if } def /Arcto { /a [ 6 -2 roll ] cvx def a r /arcto load stopped { 5 } { 4 } ifelse { pop } repeat a } def /CheckClosed { dup n 2 mul 1 sub index eq 2 index n 2 mul 1 add index eq and { pop pop /n n 1 sub def } if } def /Polygon { NArray n 2 eq { 0 0 /n 3 def } if n 3 lt { n { pop pop } repeat } { n 3 gt { CheckClosed } if n 2 mul -2 roll /y0 ED /x0 ED /y1 ED /x1 ED x1 y1 /x1 x0 x1 add 2 div def /y1 y0 y1 add 2 div def x1 y1 moveto /n n 2 sub def n { Lineto } repeat x1 y1 x0 y0 6 4 roll Lineto Lineto pop pop closepath } ifelse } def /Diamond { /mtrx CM def T rotate /h ED /w ED dup 0 eq { pop } { CLW mul neg /d ED /a w h Atan def /h d a sin Div h add def /w d a cos Div w add def } ifelse mark w 2 div h 2 div w 0 0 h neg w neg 0 0 h w 2 div h 2 div /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx setmatrix } def % DG modification begin - Jan. 15, 1997 %/Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup 0 eq { %pop } { CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 %div dup cos exch sin Div mul sub def } ifelse mark 0 d w neg d 0 h w d 0 %d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx %setmatrix } def /Triangle { /mtrx CM def translate rotate /h ED 2 div /w ED dup CLW mul /d ED /h h d w h Atan sin Div sub def /w w d h w Atan 2 div dup cos exch sin Div mul sub def mark 0 d w neg d 0 h w d 0 d /ArrowA { moveto } def /ArrowB { } def false Line closepath mtrx % DG/SR modification begin - Jun. 1, 1998 - Patch 3 (from Michael Vulis) % setmatrix } def setmatrix pop } def % DG/SR modification end /CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth def } def /CCA { /y ED /x ED 2 copy y sub /dy1 ED x sub /dx1 ED /l1 dx1 dy1 Pyth def } def /CC { /l0 l1 def /x1 x dx sub def /y1 y dy sub def /dx0 dx1 def /dy0 dy1 def CCA /dx dx0 l1 c exp mul dx1 l0 c exp mul add def /dy dy0 l1 c exp mul dy1 l0 c exp mul add def /m dx0 dy0 Atan dx1 dy1 Atan sub 2 div cos abs b exp a mul dx dy Pyth Div 2 div def /x2 x l0 dx mul m mul sub def /y2 y l0 dy mul m mul sub def /dx l1 dx mul m mul neg def /dy l1 dy mul m mul neg def } def /IC { /c c 1 add def c 0 lt { /c 0 def } { c 3 gt { /c 3 def } if } ifelse /a a 2 mul 3 div 45 cos b exp div def CCA /dx 0 def /dy 0 def } def /BOC { IC CC x2 y2 x1 y1 ArrowA CP 4 2 roll x y curveto } def /NC { CC x1 y1 x2 y2 x y curveto } def /EOC { x dx sub y dy sub 4 2 roll ArrowB 2 copy curveto } def /BAC { IC CC x y moveto CC x1 y1 CP ArrowA } def /NAC { x2 y2 x y curveto CC x1 y1 } def /EAC { x2 y2 x y ArrowB curveto pop pop } def /OpenCurve { NArray n 3 lt { n { pop pop } repeat } { BOC /n n 3 sub def n { NC } repeat EOC } ifelse } def /AltCurve { { false NArray n 2 mul 2 roll [ n 2 mul 3 sub 1 roll ] aload /Points ED n 2 mul -2 roll } { false NArray } ifelse n 4 lt { n { pop pop } repeat } { BAC /n n 4 sub def n { NAC } repeat EAC } ifelse } def /ClosedCurve { NArray n 3 lt { n { pop pop } repeat } { n 3 gt { CheckClosed } if 6 copy n 2 mul 6 add 6 roll IC CC x y moveto n { NC } repeat closepath pop pop } ifelse } def /SQ { /r ED r r moveto r r neg L r neg r neg L r neg r L fill } def /ST { /y ED /x ED x y moveto x neg y L 0 x L fill } def /SP { /r ED gsave 0 r moveto 4 { 72 rotate 0 r L } repeat fill grestore } def /FontDot { DS 2 mul dup matrix scale matrix concatmatrix exch matrix rotate matrix concatmatrix exch findfont exch makefont setfont } def /Rect { x1 y1 y2 add 2 div moveto x1 y2 lineto x2 y2 lineto x2 y1 lineto x1 y1 lineto closepath } def /OvalFrame { x1 x2 eq y1 y2 eq or { pop pop x1 y1 moveto x2 y2 L } { y1 y2 sub abs x1 x2 sub abs 2 copy gt { exch pop } { pop } ifelse 2 div exch { dup 3 1 roll mul exch } if 2 copy lt { pop } { exch pop } ifelse /b ED x1 y1 y2 add 2 div moveto x1 y2 x2 y2 b arcto x2 y2 x2 y1 b arcto x2 y1 x1 y1 b arcto x1 y1 x1 y2 b arcto 16 { pop } repeat closepath } ifelse } def /Frame { CLW mul /a ED 3 -1 roll 2 copy gt { exch } if a sub /y2 ED a add /y1 ED 2 copy gt { exch } if a sub /x2 ED a add /x1 ED 1 index 0 eq { pop pop Rect } { OvalFrame } ifelse } def /BezierNArray { /f ED counttomark 2 div dup cvi /n ED n eq not { exch pop } if n 1 sub neg 3 mod 3 add 3 mod { 0 0 /n n 1 add def } repeat f { ] aload /Points ED } { n 2 mul 1 add -1 roll pop } ifelse } def /OpenBezier { BezierNArray n 1 eq { pop pop } { ArrowA n 4 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat 6 2 roll 4 2 roll ArrowB curveto } ifelse } def /ClosedBezier { BezierNArray n 1 eq { pop pop } { moveto n 1 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat closepath } ifelse } def /BezierShowPoints { gsave Points aload length 2 div cvi /n ED moveto n 1 sub { lineto } repeat CLW 2 div SLW [ 4 4 ] 0 setdash stroke grestore } def /Parab { /y0 exch def /x0 exch def /y1 exch def /x1 exch def /dx x0 x1 sub 3 div def /dy y0 y1 sub 3 div def x0 dx sub y0 dy add x1 y1 ArrowA x0 dx add y0 dy add x0 2 mul x1 sub y1 ArrowB curveto /Points [ x1 y1 x0 y0 x0 2 mul x1 sub y1 ] def } def /Grid { newpath /a 4 string def /b ED /c ED /n ED cvi dup 1 lt { pop 1 } if /s ED s div dup 0 eq { pop 1 } if /dy ED s div dup 0 eq { pop 1 } if /dx ED dy div round dy mul /y0 ED dx div round dx mul /x0 ED dy div round cvi /y2 ED dx div round cvi /x2 ED dy div round cvi /y1 ED dx div round cvi /x1 ED /h y2 y1 sub 0 gt { 1 } { -1 } ifelse def /w x2 x1 sub 0 gt { 1 } { -1 } ifelse def b 0 gt { /z1 b 4 div CLW 2 div add def /Helvetica findfont b scalefont setfont /b b .95 mul CLW 2 div add def } if systemdict /setstrokeadjust known { true setstrokeadjust /t { } def } { /t { transform 0.25 sub round 0.25 add exch 0.25 sub round 0.25 add exch itransform } bind def } ifelse gsave n 0 gt { 1 setlinecap [ 0 dy n div ] dy n div 2 div setdash } { 2 setlinecap } ifelse /i x1 def /f y1 dy mul n 0 gt { dy n div 2 div h mul sub } if def /g y2 dy mul n 0 gt { dy n div 2 div h mul add } if def x2 x1 sub w mul 1 add dup 1000 gt { pop 1000 } if { i dx mul dup y0 moveto b 0 gt { gsave c i a cvs dup stringwidth pop /z2 ED w 0 gt {z1} {z1 z2 add neg} ifelse h 0 gt {b neg} {z1} ifelse rmoveto show grestore } if dup t f moveto g t L stroke /i i w add def } repeat grestore gsave n 0 gt % DG/SR modification begin - Nov. 7, 1997 - Patch 1 %{ 1 setlinecap [ 0 dx n div ] dy n div 2 div setdash } { 1 setlinecap [ 0 dx n div ] dx n div 2 div setdash } % DG/SR modification end { 2 setlinecap } ifelse /i y1 def /f x1 dx mul n 0 gt { dx n div 2 div w mul sub } if def /g x2 dx mul n 0 gt { dx n div 2 div w mul add } if def y2 y1 sub h mul 1 add dup 1000 gt { pop 1000 } if { newpath i dy mul dup x0 exch moveto b 0 gt { gsave c i a cvs dup stringwidth pop /z2 ED w 0 gt {z1 z2 add neg} {z1} ifelse h 0 gt {z1} {b neg} ifelse rmoveto show grestore } if dup f exch t moveto g exch t L stroke /i i h add def } repeat grestore } def /ArcArrow { /d ED /b ED /a ED gsave newpath 0 -1000 moveto clip newpath 0 1 0 0 b grestore c mul /e ED pop pop pop r a e d PtoC y add exch x add exch r a PtoC y add exch x add exch b pop pop pop pop a e d CLW 8 div c mul neg d } def /Ellipse { /mtrx CM def T scale 0 0 1 5 3 roll arc mtrx setmatrix } def /Rot { CP CP translate 3 -1 roll neg rotate NET } def /RotBegin { tx@Dict /TMatrix known not { /TMatrix { } def /RAngle { 0 } def } if /TMatrix [ TMatrix CM ] cvx def /a ED a Rot /RAngle [ RAngle dup a add ] cvx def } def /RotEnd { /TMatrix [ TMatrix setmatrix ] cvx def /RAngle [ RAngle pop ] cvx def } def /PutCoor { gsave CP T CM STV exch exec moveto setmatrix CP grestore } def /PutBegin { /TMatrix [ TMatrix CM ] cvx def CP 4 2 roll T moveto } def /PutEnd { CP /TMatrix [ TMatrix setmatrix ] cvx def moveto } def /Uput { /a ED add 2 div /h ED 2 div /w ED /s a sin def /c a cos def /b s abs c abs 2 copy gt dup /q ED { pop } { exch pop } ifelse def /w1 c b div w mul def /h1 s b div h mul def q { w1 abs w sub dup c mul abs } { h1 abs h sub dup s mul abs } ifelse } def /UUput { /z ED abs /y ED /x ED q { x s div c mul abs y gt } { x c div s mul abs y gt } ifelse { x x mul y y mul sub z z mul add sqrt z add } { q { x s div } { x c div } ifelse abs } ifelse a PtoC h1 add exch w1 add exch } def /BeginOL { dup (all) eq exch TheOL eq or { IfVisible not { Visible /IfVisible true def } if } { IfVisible { Invisible /IfVisible false def } if } ifelse } def /InitOL { /OLUnit [ 3000 3000 matrix defaultmatrix dtransform ] cvx def /Visible { CP OLUnit idtransform T moveto } def /Invisible { CP OLUnit neg exch neg exch idtransform T moveto } def /BOL { BeginOL } def /IfVisible true def } def end % END pstricks.pro %%EndProcSet %%BeginProcSet: pst-dots.pro %!PS-Adobe-2.0 %%Title: Dot Font for PSTricks 97 - Version 97, 93/05/07. %%Creator: Timothy Van Zandt %%Creation Date: May 7, 1993 10 dict dup begin /FontType 3 def /FontMatrix [ .001 0 0 .001 0 0 ] def /FontBBox [ 0 0 0 0 ] def /Encoding 256 array def 0 1 255 { Encoding exch /.notdef put } for Encoding dup (b) 0 get /Bullet put dup (c) 0 get /Circle put dup (C) 0 get /BoldCircle put dup (u) 0 get /SolidTriangle put dup (t) 0 get /Triangle put dup (T) 0 get /BoldTriangle put dup (r) 0 get /SolidSquare put dup (s) 0 get /Square put dup (S) 0 get /BoldSquare put dup (q) 0 get /SolidPentagon put dup (p) 0 get /Pentagon put (P) 0 get /BoldPentagon put /Metrics 13 dict def Metrics begin /Bullet 1000 def /Circle 1000 def /BoldCircle 1000 def /SolidTriangle 1344 def /Triangle 1344 def /BoldTriangle 1344 def /SolidSquare 886 def /Square 886 def /BoldSquare 886 def /SolidPentagon 1093.2 def /Pentagon 1093.2 def /BoldPentagon 1093.2 def /.notdef 0 def end /BBoxes 13 dict def BBoxes begin /Circle { -550 -550 550 550 } def /BoldCircle /Circle load def /Bullet /Circle load def /Triangle { -571.5 -330 571.5 660 } def /BoldTriangle /Triangle load def /SolidTriangle /Triangle load def /Square { -450 -450 450 450 } def /BoldSquare /Square load def /SolidSquare /Square load def /Pentagon { -546.6 -465 546.6 574.7 } def /BoldPentagon /Pentagon load def /SolidPentagon /Pentagon load def /.notdef { 0 0 0 0 } def end /CharProcs 20 dict def CharProcs begin /Adjust { 2 copy dtransform floor .5 add exch floor .5 add exch idtransform 3 -1 roll div 3 1 roll exch div exch scale } def /CirclePath { 0 0 500 0 360 arc closepath } def /Bullet { 500 500 Adjust CirclePath fill } def /Circle { 500 500 Adjust CirclePath .9 .9 scale CirclePath eofill } def /BoldCircle { 500 500 Adjust CirclePath .8 .8 scale CirclePath eofill } def /BoldCircle { CirclePath .8 .8 scale CirclePath eofill } def /TrianglePath { 0 660 moveto -571.5 -330 lineto 571.5 -330 lineto closepath } def /SolidTriangle { TrianglePath fill } def /Triangle { TrianglePath .85 .85 scale TrianglePath eofill } def /BoldTriangle { TrianglePath .7 .7 scale TrianglePath eofill } def /SquarePath { -450 450 moveto 450 450 lineto 450 -450 lineto -450 -450 lineto closepath } def /SolidSquare { SquarePath fill } def /Square { SquarePath .89 .89 scale SquarePath eofill } def /BoldSquare { SquarePath .78 .78 scale SquarePath eofill } def /PentagonPath { -337.8 -465 moveto 337.8 -465 lineto 546.6 177.6 lineto 0 574.7 lineto -546.6 177.6 lineto closepath } def /SolidPentagon { PentagonPath fill } def /Pentagon { PentagonPath .89 .89 scale PentagonPath eofill } def /BoldPentagon { PentagonPath .78 .78 scale PentagonPath eofill } def /.notdef { } def end /BuildGlyph { exch begin Metrics 1 index get exec 0 BBoxes 3 index get exec setcachedevice CharProcs begin load exec end end } def /BuildChar { 1 index /Encoding get exch get 1 index /BuildGlyph get exec } bind def end /PSTricksDotFont exch definefont pop % END pst-dots.pro %%EndProcSet %%BeginProcSet: pst-text.pro %! % PostScript header file pst-text.pro % Version 97, 94/04/20 % For distribution, see pstricks.tex. /tx@TextPathDict 40 dict def tx@TextPathDict begin % Syntax: PathPosition - % Function: Searches for position of currentpath distance from % beginning. Sets (X,Y)=position, and Angle=tangent. /PathPosition { /targetdist exch def /pathdist 0 def /continue true def /X { newx } def /Y { newy } def /Angle 0 def gsave flattenpath { movetoproc } { linetoproc } { } { firstx firsty linetoproc } /pathforall load stopped { pop pop pop pop /X 0 def /Y 0 def } if grestore } def /movetoproc { continue { @movetoproc } { pop pop } ifelse } def /@movetoproc { /newy exch def /newx exch def /firstx newx def /firsty newy def } def /linetoproc { continue { @linetoproc } { pop pop } ifelse } def /@linetoproc { /oldx newx def /oldy newy def /newy exch def /newx exch def /dx newx oldx sub def /dy newy oldy sub def /dist dx dup mul dy dup mul add sqrt def /pathdist pathdist dist add def pathdist targetdist ge { pathdist targetdist sub dist div dup dy mul neg newy add /Y exch def dx mul neg newx add /X exch def /Angle dy dx atan def /continue false def } if } def /TextPathShow { /String exch def /CharCount 0 def String length { String CharCount 1 getinterval ShowChar /CharCount CharCount 1 add def } repeat } def % Syntax: InitTextPath - /InitTextPath { gsave currentpoint /Y exch def /X exch def exch X Hoffset sub sub mul Voffset Hoffset sub add neg X add /Hoffset exch def /Voffset Y def grestore } def /Transform { PathPosition dup Angle cos mul Y add exch Angle sin mul neg X add exch translate Angle rotate } def /ShowChar { /Char exch def gsave Char end stringwidth tx@TextPathDict begin 2 div /Sy exch def 2 div /Sx exch def currentpoint Voffset sub Sy add exch Hoffset sub Sx add Transform Sx neg Sy neg moveto Char end tx@TextPathSavedShow tx@TextPathDict begin grestore Sx 2 mul Sy 2 mul rmoveto } def end % END pst-text.pro %%EndProcSet %%BeginProcSet: pst-node.pro %! % PostScript prologue for pst-node.tex. % Version 97 patch 1, 97/05/09. % For distribution, see pstricks.tex. % /tx@NodeDict 400 dict def tx@NodeDict begin tx@Dict begin /T /translate load def end /NewNode { gsave /next ED dict dup 3 1 roll def exch { dup 3 1 roll def } if begin tx@Dict begin STV CP T exec end /NodeMtrx CM def next end grestore } def /InitPnode { /Y ED /X ED /NodePos { NodeSep Cos mul NodeSep Sin mul } def } def /InitCnode { /r ED /Y ED /X ED /NodePos { NodeSep r add dup Cos mul exch Sin mul } def } def /GetRnodePos { Cos 0 gt { /dx r NodeSep add def } { /dx l NodeSep sub def } ifelse Sin 0 gt { /dy u NodeSep add def } { /dy d NodeSep sub def } ifelse dx Sin mul abs dy Cos mul abs gt { dy Cos mul Sin div dy } { dx dup Sin mul Cos Div } ifelse } def /InitRnode { /Y ED /X ED X sub /r ED /l X neg def Y add neg /d ED Y sub /u ED /NodePos { GetRnodePos } def } def /DiaNodePos { w h mul w Sin mul abs h Cos mul abs add Div NodeSep add dup Cos mul exch Sin mul } def /TriNodePos { Sin s lt { d NodeSep sub dup Cos mul Sin Div exch } { w h mul w Sin mul h Cos abs mul add Div NodeSep add dup Cos mul exch Sin mul } ifelse } def /InitTriNode { sub 2 div exch 2 div exch 2 copy T 2 copy 4 index index /d ED pop pop pop pop -90 mul rotate /NodeMtrx CM def /X 0 def /Y 0 def d sub abs neg /d ED d add /h ED 2 div h mul h d sub Div /w ED /s d w Atan sin def /NodePos { TriNodePos } def } def /OvalNodePos { /ww w NodeSep add def /hh h NodeSep add def Sin ww mul Cos hh mul Atan dup cos ww mul exch sin hh mul } def /GetCenter { begin X Y NodeMtrx transform CM itransform end } def /XYPos { dup sin exch cos Do /Cos ED /Sin ED /Dist ED Cos 0 gt { Dist Dist Sin mul Cos div } { Cos 0 lt { Dist neg Dist Sin mul Cos div neg } { 0 Dist Sin mul } ifelse } ifelse Do } def /GetEdge { dup 0 eq { pop begin 1 0 NodeMtrx dtransform CM idtransform exch atan sub dup sin /Sin ED cos /Cos ED /NodeSep ED NodePos NodeMtrx dtransform CM idtransform end } { 1 eq {{exch}} {{}} ifelse /Do ED pop XYPos } ifelse } def /AddOffset { 1 index 0 eq { pop pop } { 2 copy 5 2 roll cos mul add 4 1 roll sin mul sub exch } ifelse } def /GetEdgeA { NodeSepA AngleA NodeA NodeSepTypeA GetEdge OffsetA AngleA AddOffset yA add /yA1 ED xA add /xA1 ED } def /GetEdgeB { NodeSepB AngleB NodeB NodeSepTypeB GetEdge OffsetB AngleB AddOffset yB add /yB1 ED xB add /xB1 ED } def /GetArmA { ArmTypeA 0 eq { /xA2 ArmA AngleA cos mul xA1 add def /yA2 ArmA AngleA sin mul yA1 add def } { ArmTypeA 1 eq {{exch}} {{}} ifelse /Do ED ArmA AngleA XYPos OffsetA AngleA AddOffset yA add /yA2 ED xA add /xA2 ED } ifelse } def /GetArmB { ArmTypeB 0 eq { /xB2 ArmB AngleB cos mul xB1 add def /yB2 ArmB AngleB sin mul yB1 add def } { ArmTypeB 1 eq {{exch}} {{}} ifelse /Do ED ArmB AngleB XYPos OffsetB AngleB AddOffset yB add /yB2 ED xB add /xB2 ED } ifelse } def /InitNC { /b ED /a ED /NodeSepTypeB ED /NodeSepTypeA ED /NodeSepB ED /NodeSepA ED /OffsetB ED /OffsetA ED tx@NodeDict a known tx@NodeDict b known and dup { /NodeA a load def /NodeB b load def NodeA GetCenter /yA ED /xA ED NodeB GetCenter /yB ED /xB ED } if } def /LPutLine { 4 copy 3 -1 roll sub neg 3 1 roll sub Atan /NAngle ED 1 t sub mul 3 1 roll 1 t sub mul 4 1 roll t mul add /Y ED t mul add /X ED } def /LPutLines { mark LPutVar counttomark 2 div 1 sub /n ED t floor dup n gt { pop n 1 sub /t 1 def } { dup t sub neg /t ED } ifelse cvi 2 mul { pop } repeat LPutLine cleartomark } def /BezierMidpoint { /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED /y0 ED /x0 ED /t ED /cx x1 x0 sub 3 mul def /cy y1 y0 sub 3 mul def /bx x2 x1 sub 3 mul cx sub def /by y2 y1 sub 3 mul cy sub def /ax x3 x0 sub cx sub bx sub def /ay y3 y0 sub cy sub by sub def ax t 3 exp mul bx t t mul mul add cx t mul add x0 add ay t 3 exp mul by t t mul mul add cy t mul add y0 add 3 ay t t mul mul mul 2 by t mul mul add cy add 3 ax t t mul mul mul 2 bx t mul mul add cx add atan /NAngle ED /Y ED /X ED } def /HPosBegin { yB yA ge { /t 1 t sub def } if /Y yB yA sub t mul yA add def } def /HPosEnd { /X Y yyA sub yyB yyA sub Div xxB xxA sub mul xxA add def /NAngle yyB yyA sub xxB xxA sub Atan def } def /HPutLine { HPosBegin /yyA ED /xxA ED /yyB ED /xxB ED HPosEnd } def /HPutLines { HPosBegin yB yA ge { /check { le } def } { /check { ge } def } ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { dup Y check { exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark HPosEnd } def /VPosBegin { xB xA lt { /t 1 t sub def } if /X xB xA sub t mul xA add def } def /VPosEnd { /Y X xxA sub xxB xxA sub Div yyB yyA sub mul yyA add def /NAngle yyB yyA sub xxB xxA sub Atan def } def /VPutLine { VPosBegin /yyA ED /xxA ED /yyB ED /xxB ED VPosEnd } def /VPutLines { VPosBegin xB xA ge { /check { le } def } { /check { ge } def } ifelse /xxA xA def /yyA yA def mark xB yB LPutVar { 1 index X check { exit } { /yyA ED /xxA ED } ifelse } loop /yyB ED /xxB ED cleartomark VPosEnd } def /HPutCurve { gsave newpath /SaveLPutVar /LPutVar load def LPutVar 8 -2 roll moveto curveto flattenpath /LPutVar [ {} {} {} {} pathforall ] cvx def grestore exec /LPutVar /SaveLPutVar load def } def /NCCoor { /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 xA1 yA1 ] cvx def /LPutPos { LPutVar LPutLine } def /HPutPos { LPutVar HPutLine } def /VPutPos { LPutVar VPutLine } def LPutVar } def /NCLine { NCCoor tx@Dict begin ArrowA CP 4 2 roll ArrowB lineto pop pop end } def /NCLines { false NArray n 0 eq { NCLine } { 2 copy yA sub exch xA sub Atan /AngleA ED n 2 mul dup index exch index yB sub exch xB sub Atan /AngleB ED GetEdgeA GetEdgeB /LPutVar [ xB1 yB1 n 2 mul 4 add 4 roll xA1 yA1 ] cvx def mark LPutVar tx@Dict begin false Line end /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } ifelse } def /NCCurve { GetEdgeA GetEdgeB xA1 xB1 sub yA1 yB1 sub Pyth 2 div dup 3 -1 roll mul /ArmA ED mul /ArmB ED /ArmTypeA 0 def /ArmTypeB 0 def GetArmA GetArmB xA2 yA2 xA1 yA1 tx@Dict begin ArrowA end xB2 yB2 xB1 yB1 tx@Dict begin ArrowB end curveto /LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] cvx def /LPutPos { t LPutVar BezierMidpoint } def /HPutPos { { HPutLines } HPutCurve } def /VPutPos { { VPutLines } HPutCurve } def } def /NCAngles { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def xA2 yA2 mtrx transform pop xB2 yB2 mtrx transform exch pop mtrx itransform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCAngle { GetEdgeA GetEdgeB GetArmB /mtrx AngleA matrix rotate def xB2 yB2 mtrx itransform pop xA1 yA1 mtrx itransform exch pop mtrx transform /y0 ED /x0 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 x0 y0 xA1 yA1 tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 x0 y0 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCBar { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def xA2 yA2 mtrx itransform pop xB2 yB2 mtrx itransform pop sub dup 0 mtrx transform 3 -1 roll 0 gt { /yB2 exch yB2 add def /xB2 exch xB2 add def } { /yA2 exch neg yA2 add def /xA2 exch neg xA2 add def } ifelse mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCDiag { GetEdgeA GetEdgeB GetArmA GetArmB mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCDiagg { GetEdgeA GetArmA yB yA2 sub xB xA2 sub Atan 180 add /AngleB ED GetEdgeB mark xB1 yB1 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def /NCLoop { GetEdgeA GetEdgeB GetArmA GetArmB /mtrx AngleA matrix rotate def xA2 yA2 mtrx transform loopsize add /yA3 ED /xA3 ED /xB3 xB2 yB2 mtrx transform pop def xB3 yA3 mtrx itransform /yB3 ED /xB3 ED xA3 yA3 mtrx itransform /yA3 ED /xA3 ED mark ArmB 0 ne { xB1 yB1 } if xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 ArmA 0 ne { xA1 yA1 } if tx@Dict begin false Line end /LPutVar [ xB1 yB1 xB2 yB2 xB3 yB3 xA3 yA3 xA2 yA2 xA1 yA1 ] cvx def /LPutPos { LPutLines } def /HPutPos { HPutLines } def /VPutPos { VPutLines } def } def % DG/SR modification begin - May 9, 1997 - Patch 1 %/NCCircle { 0 0 NodesepA nodeA \tx@GetEdge pop xA sub 2 div dup 2 exp r %r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add %exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 %mul add dup 5 1 roll 90 sub \tx@PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED /NCCircle { NodeSepA 0 NodeA 0 GetEdge pop 2 div dup 2 exp r r mul sub abs sqrt atan 2 mul /a ED r AngleA 90 add PtoC yA add exch xA add exch 2 copy /LPutVar [ 4 2 roll r AngleA ] cvx def /LPutPos { LPutVar t 360 mul add dup 5 1 roll 90 sub PtoC 3 -1 roll add /Y ED add /X ED /NAngle ED % DG/SR modification end } def /HPutPos { LPutPos } def /VPutPos { LPutPos } def r AngleA 90 sub a add AngleA 270 add a sub tx@Dict begin /angleB ED /angleA ED /r ED /c 57.2957 r Div def /y ED /x ED } def /NCBox { /d ED /h ED /AngleB yB yA sub xB xA sub Atan def /AngleA AngleB 180 add def GetEdgeA GetEdgeB /dx d AngleB sin mul def /dy d AngleB cos mul neg def /hx h AngleB sin mul neg def /hy h AngleB cos mul def /LPutVar [ xA1 hx add yA1 hy add xB1 hx add yB1 hy add xB1 dx add yB1 dy add xA1 dx add yA1 dy add ] cvx def /LPutPos { LPutLines } def /HPutPos { xB yB xA yA LPutLine } def /VPutPos { HPutPos } def mark LPutVar tx@Dict begin false Polygon end } def /NCArcBox { /l ED neg /d ED /h ED /a ED /AngleA yB yA sub xB xA sub Atan def /AngleB AngleA 180 add def /tA AngleA a sub 90 add def /tB tA a 2 mul add def /r xB xA sub tA cos tB cos sub Div dup 0 eq { pop 1 } if def /x0 xA r tA cos mul add def /y0 yA r tA sin mul add def /c 57.2958 r div def /AngleA AngleA a sub 180 add def /AngleB AngleB a add 180 add def GetEdgeA GetEdgeB /AngleA tA 180 add yA yA1 sub xA xA1 sub Pyth c mul sub def /AngleB tB 180 add yB yB1 sub xB xB1 sub Pyth c mul add def l 0 eq { x0 y0 r h add AngleA AngleB arc x0 y0 r d add AngleB AngleA arcn } { x0 y0 translate /tA AngleA l c mul add def /tB AngleB l c mul sub def 0 0 r h add tA tB arc r h add AngleB PtoC r d add AngleB PtoC 2 copy 6 2 roll l arcto 4 { pop } repeat r d add tB PtoC l arcto 4 { pop } repeat 0 0 r d add tB tA arcn r d add AngleA PtoC r h add AngleA PtoC 2 copy 6 2 roll l arcto 4 { pop } repeat r h add tA PtoC l arcto 4 { pop } repeat } ifelse closepath /LPutVar [ x0 y0 r AngleA AngleB h d ] cvx def /LPutPos { LPutVar /d ED /h ED /AngleB ED /AngleA ED /r ED /y0 ED /x0 ED t 1 le { r h add AngleA 1 t sub mul AngleB t mul add dup 90 add /NAngle ED PtoC } { t 2 lt { /NAngle AngleB 180 add def r 2 t sub h mul t 1 sub d mul add add AngleB PtoC } { t 3 lt { r d add AngleB 3 t sub mul AngleA 2 t sub mul add dup 90 sub /NAngle ED PtoC } { /NAngle AngleA 180 add def r 4 t sub d mul t 3 sub h mul add add AngleA PtoC } ifelse } ifelse } ifelse y0 add /Y ED x0 add /X ED } def /HPutPos { LPutPos } def /VPutPos { LPutPos } def } def /Tfan { /AngleA yB yA sub xB xA sub Atan def GetEdgeA w xA1 xB sub yA1 yB sub Pyth Pyth w Div CLW 2 div mul 2 div dup AngleA sin mul yA1 add /yA1 ED AngleA cos mul xA1 add /xA1 ED /LPutVar [ xA1 yA1 m { xB w add yB xB w sub yB } { xB yB w sub xB yB w add } ifelse xA1 yA1 ] cvx def /LPutPos { LPutLines } def /VPutPos@ { LPutVar flag { 8 4 roll pop pop pop pop } { pop pop pop pop 4 2 roll } ifelse } def /VPutPos { VPutPos@ VPutLine } def /HPutPos { VPutPos@ HPutLine } def mark LPutVar tx@Dict begin /ArrowA { moveto } def /ArrowB { } def false Line closepath end } def /LPutCoor { NAngle tx@Dict begin /NAngle ED end gsave CM STV CP Y sub neg exch X sub neg exch moveto setmatrix CP grestore } def /LPut { tx@NodeDict /LPutPos known { LPutPos } { CP /Y ED /X ED /NAngle 0 def } ifelse LPutCoor } def /HPutAdjust { Sin Cos mul 0 eq { 0 } { d Cos mul Sin div flag not { neg } if h Cos mul Sin div flag { neg } if 2 copy gt { pop } { exch pop } ifelse } ifelse s add flag { r add neg } { l add } ifelse X add /X ED } def /VPutAdjust { Sin Cos mul 0 eq { 0 } { l Sin mul Cos div flag { neg } if r Sin mul Cos div flag not { neg } if 2 copy gt { pop } { exch pop } ifelse } ifelse s add flag { d add } { h add neg } ifelse Y add /Y ED } def end % END pst-node.pro %%EndProcSet %%BeginProcSet: special.pro %! 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b(t)m(w)m(o.)g(It)f(needs)g(to)h(kno)m(w)f(in)e(adv)-5 b(ance)45 b(the)f(information)e(ab)s(out)i(the)g(sizes)448 1447 y(of)c(all)f(the)h(b)s(obbins)d(that)j(are)g(to)h(b)s(e)e(placed)g (in)g(one)h(pallet,)f(b)s(efore)g(placing)g(the)448 1560 y(\014rst)44 b(b)s(obbin.)f(This)g(algorithm)g(ac)m(hiev)m(es)j(the)f (b)s(est)g(pac)m(king)f(p)s(erformance,)h(but)448 1672 y(as)e(discussed)e(later,)i(it)f(presupp)s(oses)f(conditions)g(on)i (the)f(rob)s(ot)h(that)g(migh)m(t)g(b)s(e)448 1785 y(unrealistic.)589 1903 y(The)28 b(La)m(y)m(er)g(Algorithm)f(only)g(needs)g(the)h (information)e(of)i(the)g(sizes)f(of)h(the)g(b)s(ob-)448 2016 y(bins)38 b(coming)g(in)g(the)i(next)f(m)m(ulti-tra)m(y)g(\(21)h (b)s(obbins\).)d(It)i(pac)m(ks)h(the)f(b)s(obbins)d(in)448 2129 y(indep)s(enden)m(t)29 b(stages,)k(placing)d(on)g(the)i(pallet)e (the)h(b)s(obbins)d(of)j(one)h(m)m(ulti-tra)m(y)e(b)s(e-)448 2242 y(fore)j(considering)e(the)h(ones)h(on)f(the)h(next)g(m)m (ulti-tra)m(y)-8 b(.)33 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b(to)h(considering)e(that)i(at)g (some)g(momen)m(ts)g(of)g(the)g(pac)m(king)f(t)m(w)m(o)i(full)448 3262 y(m)m(ulti-tra)m(ys)30 b(\(with)g(21)h(b)s(obbins)c(eac)m(h\))32 b(are)f(presen)m(t.)448 3698 y Ff(2)135 b(Description)46 b(of)f(the)g(Algorithms)448 3913 y Fb(2.1)113 b(The)37 b(General)h(Algorithm)448 4094 y Fg(The)25 b(algorithm)e(supp)s(oses)g (that)j(the)f(information)e(ab)s(out)h(the)h(sizes)g(of)g(a)g(large)g (n)m(um-)448 4207 y(b)s(er)20 b(of)h(b)s(obbins)e(that)i(p)s(oten)m (tially)f(\014t)h(on)g(the)g(curren)m(t)g(pallet)f(is)g(kno)m(wn.)h (Considering)448 4320 y(that)h(9cm)f(is)f(the)h(smallest)f(b)s(obbin)e (diameter)j(and)f(that)h(the)g(pallets)f(are)h(100)q Fe(\002)q Fg(120cm)448 4433 y(rectangles,)37 b(these)g(can)g(mean)f (information)f(ab)s(out)g(up)h(to)h(160)g(b)s(obbins)c(that)k(has)448 4546 y(to)29 b(b)s(e)f(kno)m(wn)g(b)s(efore)f(the)i(p)s(osition)d(of)j (an)m(y)f(of)g(them)h(can)f(b)s(e)g(computed.)g(A)g(further)448 4658 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Black Black 589 573 a Fg(In)24 b(spite)g(of)h(these)g(facts)g (w)m(e)g(include)e(this)g(algorithm)h(since)g(it)g(pro)m(vides)f(the)i (base)448 686 y(for)36 b(the)g(other)g(t)m(w)m(o)i(and)d(moreo)m(v)m (er,)j(its)d(p)s(erformance)h(with)e(b)s(obbins)f(of)k(di\013eren)m(t) 448 799 y(sizes)27 b(pro)m(vides)f(a)h(go)s(o)s(d)g(b)s(enc)m(hmark)f (to)h(compare)g(the)h(o)s(ccupancy)e(ac)m(hiev)m(ed)i(b)m(y)f(the)448 912 y(more)k(realistic)e(Algorithms)g(2)i(and)e(3.)589 1029 y(The)g(general)h(idea)f(of)g(the)h(algorithm)e(is)h(to)h(place)f (virtually)e(a)j(set)g(of)g(circles)e(on)448 1142 y(a)39 b(rectangle)g(that)g(initially)c(is)i(m)m(uc)m(h)i(larger)f(than)g(the) g(real)g(pallet.)g(On)g(di\013eren)m(t)448 1255 y(re\014nemen)m(t)27 b(steps)f(the)h(circles)e(are)i(shifted)e(b)m(y)i(a)g(small)e(amoun)m (t)i(in)e(the)i(direction)e(of)448 1368 y(the)33 b(middle)d(of)j(the)f (rectangle)i(and)e(when)f(the)i(rectangle)g(sides)e(do)i(not)g(touc)m (h)g(an)m(y)448 1481 y(of)28 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stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 57.61662 139.39134 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 70.42027 139.39134 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 83.22392 139.39134 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 96.02757 139.39134 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 108.83122 139.39134 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 121.63486 139.39134 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 134.4385 139.39134 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 12.80363 150.47357 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 25.60728 150.47357 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 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gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 96.02757 161.55449 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 108.83122 161.55449 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 121.63486 161.55449 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial @beginspecial @setspecial tx@Dict begin STP newpath 0.28453 SLW 0 setgray 134.4385 161.55449 6.40204 .5 CLW mul sub 0 360 arc closepath gsave 0.28453 SLW 0 setgray 0 setlinecap stroke grestore end @endspecial 448 2095 a Fg(Figure)34 b(5:)h(Hexagonal)h(pac)m(king)e(with)f(9cm)i(diameter)f(circles.)f (Occupancy=83.72)448 2208 y(p)s(ercen)m(t.)p Black 448 2583 a(t)m(w)m(o)39 b(kinds)c(of)j(regular)e(pac)m(kings)h(that)h(w)m (ork)g(w)m(ell)e(for)h(the)g(case)i(of)e(circles)f(of)i(the)448 2696 y(same)31 b(radius:)e(the)h(square)h(and)e(hexagonal)i(grids.)589 2810 y(The)22 b Fa(square)j(grid)d Fg(is)f(obtained)h(b)m(y)f(placing)g (the)h(circles)f(\\on)h(top)g(of)g(eac)m(h)h(other")448 2923 y(as)28 b(sho)m(wn)e(in)g(Figure)h(4.)h(The)f(b)s(est)g(o)s (ccupancy)g(for)g(this)f(pac)m(king)h(is)f(obtained)h(when)448 3035 y(the)45 b(diameter)f(of)g(the)h(circles)e(divides)f(the)j(length) f(of)g(b)s(oth)g(rectangle)h(sides.)f(If)448 3148 y(this)25 b(condition)g(holds,)g(the)h(o)s(ccupancy)g(ac)m(hiev)m(ed)h(is)e (appro)m(ximately)h(78,53)i(p)s(ercen)m(t)448 3261 y(indep)s(enden)m (tly)19 b(of)i(the)h(circle)f(size.)g(Without)g(this)g(condition)f(the) h(o)s(ccupancy)h(can)g(b)s(e)448 3374 y(m)m(uc)m(h)32 b(w)m(orse,)g(for)f(example)g(for)g(22cm)h(diameter)f(circles)f(the)i (o)s(ccupancy)f(ac)m(hiev)m(ed)448 3487 y(is)f(ab)s(out)g(63)p Fc(:)p Fg(35\045.)589 3600 y(The)37 b Fa(hexagonal)42 b(grid)37 b Fg(sho)m(wn)f(in)g(Figure)g(5)h(is)f(obtained)g(b)m(y)g (placing)g(a)h(\014rst)448 3713 y(ro)m(w)24 b(of)g(circles)e(at)j(the)e (b)s(ottom)h(of)g(the)g(rectangle)g(starting)g(at)g(the)g(left)f(side)f (and)h(then)448 3826 y(placing)32 b(further)g(ro)m(ws)h(on)h(top)f (shifted)f(in)g(one)h(direction)f(b)m(y)h(the)h(radius)d(size.)i(F)-8 b(or)448 3939 y(the)25 b(range)g(of)g(diameters)f(considered)f(here)i (\(b)s(et)m(w)m(een)g(9)g(and)f(28cm\),)i(the)f(maxim)m(um)448 4052 y(o)s(ccupancy)i(is)e(ac)m(hiev)m(ed)i(with)e(9cm)i(diameter)f (circles.)g(In)g(this)f(case)i(the)g(o)s(ccupancy)448 4165 y(is)g(appro)m(ximately)h(83.76)i(p)s(ercen)m(t.)e(Again,)g(for)g (other)g(circle)f(size)h(the)g(o)s(ccupancy)g(is)448 4278 y(w)m(orse.)34 b(F)-8 b(or)33 b(example,)f(for)h(22cm)g(diameter)g (circles,)f(the)h(hexagonal)g(grid)e(ac)m(hiev)m(es)448 4391 y(an)g(o)s(ccupancy)f(of)h(ab)s(out)f(76)p Fc(:)p Fg(02\045.)589 4504 y(These)22 b(t)m(w)m(o)g(examples)g(of)f(pac)m (king)h(strategies)g(can)g(only)e(b)s(e)h(uses)g(in)f(case)j(of)f (equal)448 4617 y(size)30 b(circles,)f(but)g(giv)m(e)h(an)f(indication) f(to)i(estimate)h(the)e(qualit)m(y)g(of)h(our)f(algorithms)448 4730 y(for)h(v)-5 b(ariable)30 b(size)g(circles.)448 5019 y Ff(4)135 b(Conclusions)448 5223 y Fg(W)-8 b(e)27 b(ha)m(v)m(e)g(dev)m(elop)s(ed)e(three)h(algorithms)f(for)g(the)h (problem)e(of)i(pac)m(king)g(v)-5 b(ariable)24 b(size)448 5336 y(b)s(obbins.)31 b(The)j(General)f(Algorithm)g(ac)m(hiev)m(es)i(v) m(ery)f(go)s(o)s(d)g(o)s(ccupancy)f(results,)g(on)448 5449 y(a)m(v)m(erage)i(o)m(v)m(er)f(75\045)f(for)g(b)s(obbins)c(of)k (up)e(to)i(20cm)h(diameter,)e(and)g(o)m(v)m(er)i(70\045)f(when)p Black 1920 5698 a(8)p Black eop %%Page: 9 9 9 8 bop Black Black 448 573 a Fg(bigger)43 b(b)s(obbins)c(can)44 b(arriv)m(e.)e(This)f(algorithm)h(ho)m(w)m(ev)m(er)i(needs)f(to)g (\\reserv)m(e")h(in)448 686 y(adv)-5 b(ance)38 b(all)f(the)h(b)s (obbins)c(to)k(b)s(e)f(pac)m(k)m(ed)i(and)e(moreo)m(v)m(er,)i(the)f (optimal)e(order)h(in)448 799 y(whic)m(h)23 b(the)i(b)s(obbins)d (should)g(b)s(e)i(pac)m(k)m(ed)h(b)m(y)g(the)f(rob)s(ot)g(migh)m(t)h (not)f(corresp)s(ond)f(with)448 912 y(the)31 b(order)f(in)f(whic)m(h)g (the)h(b)s(obbins)e(arriv)m(e)i(on)g(the)h(m)m(ulti-tra)m(ys.)589 1024 y(The)k(La)m(y)m(er)h(and)e(Bu\013er)g(algorithms)g(are)h(more)g (realistic)f(since)g(in)f(b)s(oth)h(cases)448 1137 y(the)24 b(b)s(obbins)c(can)j(b)s(e)g(placed)f(on)h(the)h(pallet)e(in)g(an)m(y)h (desired)f(order)g(\(for)i(example)e(left)448 1250 y(to)i(righ)m(t)e (and)g(b)s(ottom)h(to)h(top\).)g(The)e(La)m(y)m(er)i(Algorithm)d(in)h (its)g Fc(b)h Fg(v)-5 b(arian)m(t)22 b(ac)m(hiev)m(es)i(on)448 1363 y(a)m(v)m(erage)36 b(an)c(o)s(ccupancy)h(of)f(ab)s(out)h(3\045)f (less)g(that)h(the)g(General)g(Algorithm,)e(whic)m(h)448 1476 y(w)m(e)g(consider)e(to)j(b)s(e)d(a)i(go)s(o)s(d)f(p)s (erformance.)589 1589 y(The)j(Bu\013er)h(Algorithm)e(can)h(store)h (temp)s(orarily)e(some)i(of)f(the)h(b)s(obbins)c(in)i(an)448 1702 y(extra)26 b(bu\013er.)e(F)-8 b(or)25 b(a)h(bu\013er)d(of)i(size)g (10,)h(only)e(in)f(a)j(v)m(ery)f(few)f(cases)i(is)e(the)h(o)s(ccupancy) 448 1815 y(ac)m(hiev)m(ed)d(b)m(y)f(this)f(algorithm)g(b)s(etter)h (than)f(the)i(one)f(from)f(the)h Fc(b)g Fg(v)m(ersion)g(of)g(the)g(La)m (y)m(er)448 1928 y(Algorithm)32 b(and)h(therefore)g(w)m(e)h(consider)e (this)g(bu\013er)g(not)i(to)f(b)s(e)g(really)f(necessary)-8 b(.)448 2041 y(F)g(or)37 b(a)f(bu\013er)e(of)i(size)g(21,)g(the)g (algorithm)f(presen)m(ts)g(an)h(o)s(ccupancy)g(impro)m(v)m(emen)m(t)448 2154 y(o)m(v)m(er)c(the)e Fc(b)g Fg(v)m(ersion)g(of)g(the)g(La)m(y)m (er)i(Algorithm)c(of)j(ab)s(out)f(1\045)g(for)g(the)g(case)h(of)g (small)448 2267 y(diameter)40 b(circles)g(\(up)g(to)h(a)g(diameter)f (of)h(ab)s(out)f(19cm\).)i(F)-8 b(or)41 b(larger)f(circles)g(the)448 2379 y(o)s(ccupancy)31 b(is)e(not)i(b)s(etter)f(than)g(that)h(of)g(the) f(La)m(y)m(er)i(Algorithm.)589 2492 y(All)g(the)g(algorithms)g(w)m(ork) h(v)m(ery)f(fast.)i(The)e(execution)g(times)h(sho)m(wn)f(with)f(the)448 2605 y(tests)39 b(are)e(measured)g(on)h(a)f(small)f(p)s(ersonal)g (computer)i(with)e(a)i(P)m(en)m(tium)f(I)s(I)s(I)f(and)448 2718 y(600)f(MHz)f(pro)s(cessor.)f(A)h(single)e(execution)i(of)f(one)h (of)f(the)h(algorithms)e(tak)m(es)j(only)448 2831 y(a)c(few)f(seconds)h (\(less)f(than)g(10\).)589 2944 y(It)c(can)g(b)s(e)e(seen)i(from)f(our) g(results)f(that)i(the)f(algorithms)g(w)m(ork)g(b)s(etter)g(when)g(the) 448 3057 y(b)s(obbins)35 b(ha)m(v)m(e)40 b(relativ)m(e)e(small)f (diameter)g(\(up)h(to)g(appro)m(x.)h(20cm\).)g(In)f(case)h(there)448 3170 y(are)29 b(b)s(obbins)d(of)j(larger)f(size,)h(it)f(do)s(es)g(not)h (matter)h(if)d(they)i(come)h(mixed)d(with)h(small)448 3283 y(b)s(obbins.)e(On)h(the)h(con)m(trary)-8 b(,)30 b(the)e(o)s(ccupancy)g(results)f(b)s(ecome)i(b)s(etter)f(in)f(this)g (case.)448 3569 y Ff(5)180 b(Occupancy)44 b(T)-11 b(ests)448 3772 y Fg(W)j(e)37 b(presen)m(t)f(the)f(o)s(ccupancy)h(results)e(for)h (the)h(di\013eren)m(t)f(algorithms)f(obtained)h(b)m(y)448 3885 y(computer)24 b(sim)m(ulations.)f(W)-8 b(e)25 b(ha)m(v)m(e)h(done) e(for)g(eac)m(h)h(one)g(of)f(the)h(algorithms)e(\(General)448 3998 y(Algorithm,)32 b(v)m(ersions)g Fc(a)h Fg(and)f Fc(b)g Fg(of)h(the)g(La)m(y)m(er)h(Algorithm,)e(and)g(Bu\013er)g (Algorithm)448 4111 y(with)27 b(a)h(bu\013er)f(of)h(size)f(10)i(and)e (20\))i(and)e(for)h(eac)m(h)h(in)m(terv)-5 b(al)27 b(for)g(the)h(p)s (ossible)d(diame-)448 4224 y(ter)i(of)f(the)g(b)s(obbins,)d Fa(25)k Fg(sim)m(ulations.)d(In)h(the)i(sim)m(ulations)d(the)i(b)s (obbins)d(sizes)j(w)m(ere)448 4337 y(generated)33 b(at)f(random)e (under)g(a)i(uniform)d(distribution)f(of)j(the)h(p)s(ossible)d(v)-5 b(alues)30 b(in)448 4450 y(the)41 b(in)m(terv)-5 b(al.)40 b(The)f(in)m(terv)-5 b(als)40 b(are)g(divided)e(in)h(three)i(groups:)e (the)i(small)e(ones)h(\(a)448 4562 y(di\013erence)28 b(of)g(1)g(and)g(1.5cm\),)i(medium)c(\(a)j(di\013erence)e(of)h(3cm\))h (and)f(large)g(in)m(terv)-5 b(als)448 4675 y(\(di\013erence)30 b(larger)g(that)h(3cm\).)h(W)-8 b(e)31 b(giv)m(e)g(the)f(data)h(for)g (the)f(w)m(orst,)h(b)s(est)f(and)f(a)m(v)m(er-)448 4788 y(age)36 b(o)s(ccupancy)f(results)f(for)g(the)h(25)h(sim)m(ulation.)d (In)h(paren)m(thesis)g(w)m(e)h(include)e(the)448 4901 y(n)m(um)m(b)s(er)c(of)i(b)s(obbins)c(pac)m(k)m(ed)32 b(in)d(eac)m(h)i(one)g(of)g(the)f(cases.)p Black 1920 5698 a(9)p Black eop %%Page: 10 10 10 9 bop Black Black Black Black 1585 573 a Fa(Small)34 b(In)m(terv)-6 b(als)p 448 684 3123 4 v 446 797 4 113 v 498 763 a Fg(Diameter)p 914 797 V 1420 797 V 1203 w(Occupancy)p 3148 797 V 695 w(Av)m(erage)p 3569 797 V 1422 800 1729 4 v 446 910 4 113 v 533 876 a(in)m(terv)h(al)p 914 910 V 965 817 a(Algorithm)p 1420 910 V 1491 876 a(W)d(orst)31 b(case)p 1988 910 V 170 w(Best)g(case)p 2556 910 V 237 w(Av)m(erage)p 3148 910 V 259 w(time)p 3569 910 V 448 913 3123 4 v 448 930 V 446 1043 4 113 v 914 1043 V 965 1009 a(General)p 1420 1043 V 198 w(77.7)101 b(\(130\))p 1988 1043 V 102 w(78.3)g(\(134\))p 2556 1043 V 102 w Fa(78)181 b Fg(\(132\))p 3148 1043 V 222 w(3s)p 3569 1043 V 916 1046 2656 4 v 446 1156 4 113 v 914 1156 V 965 1122 a(La)m(y)m(er)32 b Fc(a)p 1420 1156 V 207 w Fg(73.9)101 b(\(125\))p 1988 1156 V 102 w(75.4)g(\(127\))p 2556 1156 V 102 w Fa(74.5)f Fg(\(125\))p 3148 1156 V 222 w(4s)p 3569 1156 V 916 1159 2656 4 v 446 1269 4 113 v 591 1235 a(9{10)p 914 1269 V 194 w(La)m(y)m(er)32 b Fc(b)p 1420 1269 V 216 w Fg(74.2)101 b(\(126\))p 1988 1269 V 102 w(76.8)g(\(130\))p 2556 1269 V 102 w Fa(75.6)f Fg(\(128\))p 3148 1269 V 222 w(6s)p 3569 1269 V 916 1272 2656 4 v 446 1381 4 113 v 914 1381 V 965 1348 a(Bu\013er)31 b(10)p 1420 1381 V 142 w(73.8)101 b(\(125\))p 1988 1381 V 102 w(76.1)g(\(129\))p 2556 1381 V 102 w Fa(75)181 b Fg(\(127\))p 3148 1381 V 222 w(8s)p 3569 1381 V 916 1385 2656 4 v 446 1494 4 113 v 914 1494 V 965 1461 a(Bu\013er)31 b(21)p 1420 1494 V 142 w(73.9)101 b(\(126\))p 1988 1494 V 102 w(75)171 b(\(127\))p 2556 1494 V 102 w Fa(74.6)100 b Fg(\(132\))p 3148 1494 V 222 w(2s)p 3569 1494 V 448 1498 3123 4 v 448 1514 V 446 1627 4 113 v 914 1627 V 965 1593 a(General)p 1420 1627 V 198 w(77.7)h(\(107\))p 1988 1627 V 102 w(78.4)g(\(110\))p 2556 1627 V 102 w Fa(78)181 b Fg(\(108\))p 3148 1627 V 222 w(3s)p 3569 1627 V 916 1631 2656 4 v 446 1740 4 113 v 914 1740 V 965 1706 a(La)m(y)m(er)32 b Fc(a)p 1420 1740 V 207 w Fg(72.5)101 b(\(101\))p 1988 1740 V 102 w(75.7)g(\(105\))p 2556 1740 V 102 w Fa(74.4)f Fg(\(103\))p 3148 1740 V 222 w(5s)p 3569 1740 V 916 1743 2656 4 v 446 1853 4 113 v 568 1819 a(10{11)p 914 1853 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 1853 V 216 w Fg(72.4)101 b(\(101\))p 1988 1853 V 102 w(75.5)g(\(105\))p 2556 1853 V 102 w Fa(74.4)f Fg(\(103\))p 3148 1853 V 222 w(4s)p 3569 1853 V 916 1856 2656 4 v 446 1966 4 113 v 914 1966 V 965 1932 a(Bu\013er)31 b(10)p 1420 1966 V 142 w(69.3)147 b(\(95\))p 1988 1966 V 101 w(75.7)101 b(\(105\))p 2556 1966 V 102 w Fa(72.6)f Fg(\(100\))p 3148 1966 V 222 w(6s)p 3569 1966 V 916 1969 2656 4 v 446 2079 4 113 v 914 2079 V 965 2045 a(Bu\013er)31 b(21)p 1420 2079 V 142 w(74.2)101 b(\(103\))p 1988 2079 V 102 w(76.3)g(\(105\))p 2556 2079 V 102 w Fa(75.4)f Fg(\(104\))p 3148 2079 V 222 w(2s)p 3569 2079 V 448 2082 3123 4 v 448 2099 V 446 2212 4 113 v 914 2212 V 965 2178 a(General)p 1420 2212 V 198 w(77.2)147 b(\(89\))p 1988 2212 V 101 w(78.5)g(\(91\))p 2556 2212 V 101 w Fa(77.9)f Fg(\(90\))p 3148 2212 V 221 w(3s)p 3569 2212 V 916 2215 2656 4 v 446 2325 4 113 v 914 2325 V 965 2291 a(La)m(y)m(er)32 b Fc(a)p 1420 2325 V 207 w Fg(71.8)147 b(\(84\))p 1988 2325 V 101 w(74)217 b(\(86\))p 2556 2325 V 101 w Fa(72.9)146 b Fg(\(84\))p 3148 2325 V 221 w(3s)p 3569 2325 V 916 2328 2656 4 v 446 2438 4 113 v 568 2404 a(11{12)p 914 2438 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 2438 V 216 w Fg(73)217 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3460 a(La)m(y)m(er)32 b Fc(a)p 1420 3494 V 207 w Fg(72.9)147 b(\(61\))p 1988 3494 V 101 w(75.5)g(\(63\))p 2556 3494 V 101 w Fa(74.9)f Fg(\(62\))p 3148 3494 V 221 w(3s)p 3569 3494 V 916 3497 2656 4 v 446 3606 4 113 v 568 3573 a(13{14)p 914 3606 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 3606 V 216 w Fg(72.6)147 b(\(61\))p 1988 3606 V 101 w(77.7)g(\(66\))p 2556 3606 V 101 w Fa(75.2)f Fg(\(63\))p 3148 3606 V 221 w(4s)p 3569 3606 V 916 3610 2656 4 v 446 3719 4 113 v 914 3719 V 965 3686 a(Bu\013er)31 b(10)p 1420 3719 V 142 w(71.3)147 b(\(60\))p 1988 3719 V 101 w(75.9)g(\(64\))p 2556 3719 V 101 w Fa(73)227 b Fg(\(61\))p 3148 3719 V 221 w(4s)p 3569 3719 V 916 3723 2656 4 v 446 3832 4 113 v 914 3832 V 965 3798 a(Bu\013er)31 b(21)p 1420 3832 V 142 w(74.3)147 b(\(63\))p 1988 3832 V 101 w(76.6)g(\(65\))p 2556 3832 V 101 w Fa(75.2)f Fg(\(63\))p 3148 3832 V 221 w(1s)p 3569 3832 V 448 3836 3123 4 v 448 3852 V 446 3965 4 113 v 914 3965 V 965 3931 a(General)p 1420 3965 V 198 w(75.1)h(\(55\))p 1988 3965 V 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3020 4596 V 221 w(1s)p 3440 4596 V 916 4599 2527 4 v 446 4709 4 113 v 914 4709 V 965 4675 a(La)m(y)m(er)32 b Fc(a)p 1420 4709 V 207 w Fg(68.2)109 b(\(19\))p 1951 4709 V 101 w(72.6)101 b(\(20\))p 2473 4709 V 102 w Fa(70.2)f Fg(\(19\))p 3020 4709 V 221 w(1s)p 3440 4709 V 916 4712 2527 4 v 446 4822 4 113 v 568 4788 a(23{24)p 914 4822 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 4822 V 216 w Fg(68.2)109 b(\(19\))p 1951 4822 V 101 w(72.5)101 b(\(20\))p 2473 4822 V 102 w Fa(70.7)f Fg(\(19\))p 3020 4822 V 221 w(2s)p 3440 4822 V 916 4825 2527 4 v 446 4935 4 113 v 914 4935 V 965 4901 a(Bu\013er)31 b(10)p 1420 4935 V 142 w(68)179 b(\(19\))p 1951 4935 V 101 w(71.8)101 b(\(20\))p 2473 4935 V 102 w Fa(69.1)f Fg(\(19\))p 3020 4935 V 221 w(2s)p 3440 4935 V 916 4938 2527 4 v 446 5048 4 113 v 914 5048 V 965 5014 a(Bu\013er)31 b(21)p 1420 5048 V 142 w(68.2)109 b(\(19\))p 1951 5048 V 101 w(72.5)101 b(\(20\))p 2473 5048 V 102 w Fa(70.3)f Fg(\(19\))p 3020 5048 V 221 w(1s)p 3440 5048 V 448 5051 2994 4 v 448 5068 V 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3052 V 221 w(1s)p 3440 3052 V 916 3055 2527 4 v 446 3165 4 113 v 914 3165 V 965 3131 a(La)m(y)m(er)32 b Fc(a)p 1420 3165 V 207 w Fg(67.5)109 b(\(25\))p 1951 3165 V 101 w(72,6)101 b(\(27\))p 2473 3165 V 102 w Fa(70)181 b Fg(\(26\))p 3020 3165 V 221 w(1s)p 3440 3165 V 916 3168 2527 4 v 446 3278 4 113 v 533 3244 a(19.5{21)p 914 3278 V 137 w(La)m(y)m(er)32 b Fc(b)p 1420 3278 V 216 w Fg(69.9)109 b(\(26\))p 1951 3278 V 101 w(75)171 b(\(28\))p 2473 3278 V 102 w Fa(73.2)100 b Fg(\(27\))p 3020 3278 V 221 w(2s)p 3440 3278 V 916 3281 2527 4 v 446 3391 4 113 v 914 3391 V 965 3357 a(Bu\013er)31 b(10)p 1420 3391 V 142 w(69.4)109 b(\(26\))p 1951 3391 V 101 w(74.5)101 b(\(28\))p 2473 3391 V 102 w Fa(71.5)f Fg(\(26\))p 3020 3391 V 221 w(2s)p 3440 3391 V 916 3394 2527 4 v 446 3504 4 113 v 914 3504 V 965 3470 a(Bu\013er)31 b(21)p 1420 3504 V 142 w(71.6)109 b(\(27\))p 1951 3504 V 101 w(74.1)101 b(\(28\))p 2473 3504 V 102 w Fa(72.7)f Fg(\(27\))p 3020 3504 V 221 w(2s)p 3440 3504 V 448 3507 2994 4 v 448 3523 V 446 3636 4 113 v 914 3636 V 965 3602 a(General)p 1420 3636 V 198 w(73.4)109 b(\(24\))p 1951 3636 V 101 w(77.6)101 b(\(25\))p 2473 3636 V 102 w Fa(75.7)f Fg(\(24\))p 3020 3636 V 221 w(1s)p 3440 3636 V 916 3640 2527 4 v 446 3749 4 113 v 914 3749 V 965 3715 a(La)m(y)m(er)32 b Fc(a)p 1420 3749 V 207 w Fg(64.1)109 b(\(21\))p 1951 3749 V 101 w(72)171 b(\(23\))p 2473 3749 V 102 w Fa(67.1)100 b Fg(\(21\))p 3020 3749 V 221 w(1s)p 3440 3749 V 916 3753 2527 4 v 446 3862 4 113 v 533 3828 a(21{22.5)p 914 3862 V 137 w(La)m(y)m(er)32 b Fc(b)p 1420 3862 V 216 w Fg(67.9)109 b(\(22\))p 1951 3862 V 101 w(75.3)101 b(\(24\))p 2473 3862 V 102 w Fa(72.1)f Fg(\(23\))p 3020 3862 V 221 w(1s)p 3440 3862 V 916 3866 2527 4 v 446 3975 4 113 v 914 3975 V 965 3941 a(Bu\013er)31 b(10)p 1420 3975 V 142 w(67)179 b(\(22\))p 1951 3975 V 101 w(73.5)101 b(\(24\))p 2473 3975 V 102 w Fa(69.1)f Fg(\(22\))p 3020 3975 V 221 w(1s)p 3440 3975 V 916 3978 2527 4 v 446 4088 4 113 v 914 4088 V 965 4054 a(Bu\013er)31 b(21)p 1420 4088 V 142 w(70.2)109 b(\(23\))p 1951 4088 V 101 w(74.6)101 b(\(24\))p 2473 4088 V 102 w Fa(72)181 b Fg(\(23\))p 3020 4088 V 221 w(2s)p 3440 4088 V 448 4091 2994 4 v 448 4108 V 446 4221 4 113 v 914 4221 V 965 4187 a(General)p 1420 4221 V 198 w(69.8)109 b(\(20\))p 1951 4221 V 101 w(74)171 b(\(21\))p 2473 4221 V 102 w Fa(71.1)100 b Fg(\(20\))p 3020 4221 V 221 w(1s)p 3440 4221 V 916 4224 2527 4 v 446 4334 4 113 v 914 4334 V 965 4300 a(La)m(y)m(er)32 b Fc(a)p 1420 4334 V 207 w Fg(66.4)109 b(\(19\))p 1951 4334 V 101 w(74.1)101 b(\(21\))p 2473 4334 V 102 w Fa(70.9)f Fg(\(20\))p 3020 4334 V 221 w(1s)p 3440 4334 V 916 4337 2527 4 v 446 4447 4 113 v 533 4413 a(22.5{24)p 914 4447 V 137 w(La)m(y)m(er)32 b Fc(b)p 1420 4447 V 216 w Fg(66.5)109 b(\(19\))p 1951 4447 V 101 w(73.1)101 b(\(21\))p 2473 4447 V 102 w Fa(70.7)f Fg(\(20\))p 3020 4447 V 221 w(1s)p 3440 4447 V 916 4450 2527 4 v 446 4560 4 113 v 914 4560 V 965 4526 a(Bu\013er)31 b(10)p 1420 4560 V 142 w(63)179 b(\(18\))p 1951 4560 V 101 w(71.8)101 b(\(20\))p 2473 4560 V 102 w Fa(69.1)f Fg(\(19\))p 3020 4560 V 221 w(2s)p 3440 4560 V 916 4563 2527 4 v 446 4672 4 113 v 914 4672 V 965 4639 a(Bu\013er)31 b(21)p 1420 4672 V 142 w(67.1)109 b(\(19\))p 1951 4672 V 101 w(71.8)101 b(\(20\))p 2473 4672 V 102 w Fa(70.5)f Fg(\(19\))p 3020 4672 V 221 w(1s)p 3440 4672 V 448 4676 2994 4 v 448 4692 V 446 4805 4 113 v 914 4805 V 965 4771 a(General)p 1420 4805 V 198 w(69)179 b(\(17\))p 1951 4805 V 101 w(75.1)101 b(\(19\))p 2473 4805 V 102 w Fa(72.2)f Fg(\(18\))p 3020 4805 V 221 w(1s)p 3440 4805 V 916 4809 2527 4 v 446 4918 4 113 v 914 4918 V 965 4884 a(La)m(y)m(er)32 b Fc(a)p 1420 4918 V 207 w Fg(67.9)109 b(\(17\))p 1951 4918 V 101 w(75.9)101 b(\(19\))p 2473 4918 V 102 w Fa(70.8)f Fg(\(17\))p 3020 4918 V 221 w(1s)p 3440 4918 V 916 4922 2527 4 v 446 5031 4 113 v 533 4997 a(24{25.5)p 914 5031 V 137 w(La)m(y)m(er)32 b Fc(b)p 1420 5031 V 216 w Fg(68.1)109 b(\(17\))p 1951 5031 V 101 w(76.6)101 b(\(19\))p 2473 5031 V 102 w Fa(72.2)f Fg(\(18\))p 3020 5031 V 221 w(2s)p 3440 5031 V 916 5034 2527 4 v 446 5144 4 113 v 914 5144 V 965 5110 a(Bu\013er)31 b(10)p 1420 5144 V 142 w(69.4)109 b(\(17\))p 1951 5144 V 101 w(76.7)101 b(\(19\))p 2473 5144 V 102 w Fa(72.3)f Fg(\(18\))p 3020 5144 V 221 w(2s)p 3440 5144 V 916 5147 2527 4 v 446 5257 4 113 v 914 5257 V 965 5223 a(Bu\013er)31 b(21)p 1420 5257 V 142 w(67.7)109 b(\(17\))p 1951 5257 V 101 w(76.4)101 b(\(19\))p 2473 5257 V 102 w Fa(71.8)f Fg(\(17\))p 3020 5257 V 221 w(1s)p 3440 5257 V 448 5260 2994 4 v Black 1897 5698 a(13)p Black eop %%Page: 14 14 14 13 bop Black Black 448 485 2994 4 v 446 598 4 113 v 498 564 a Fg(Diameter)p 914 598 V 1420 598 V 1138 w(Occupancy)p 3020 598 V 631 w(Av)m(erage)p 3440 598 V 1422 601 1600 4 v 446 711 4 113 v 533 677 a(in)m(terv)-5 b(al)p 914 711 V 965 618 a(Algorithm)p 1420 711 V 1472 677 a(W)d(orst)31 b(case)p 1951 711 V 128 w(Best)h(case)p 2473 711 V 191 w(Av)m(erage)p 3020 711 V 236 w(time)p 3440 711 V 448 714 2994 4 v 448 731 V 448 734 V 448 751 V 446 863 4 113 v 914 863 V 965 830 a(General)p 1420 863 V 198 w(70.6)109 b(\(16\))p 1951 863 V 101 w(73.4)101 b(\(16\))p 2473 863 V 102 w Fa(72)181 b Fg(\(16\))p 3020 863 V 221 w(1s)p 3440 863 V 916 867 2527 4 v 446 976 4 113 v 914 976 V 965 942 a(La)m(y)m(er)32 b Fc(a)p 1420 976 V 207 w Fg(67)179 b(\(15\))p 1951 976 V 101 w(73.1)101 b(\(16\))p 2473 976 V 102 w Fa(70.5)f Fg(\(15\))p 3020 976 V 221 w(1s)p 3440 976 V 916 980 2527 4 v 446 1089 4 113 v 533 1055 a(25.5{27)p 914 1089 V 137 w(La)m(y)m(er)32 b Fc(b)p 1420 1089 V 216 w Fg(66.9)109 b(\(15\))p 1951 1089 V 101 w(72.8)101 b(\(16\))p 2473 1089 V 102 w Fa(70)181 b Fg(\(15\))p 3020 1089 V 221 w(2s)p 3440 1089 V 916 1093 2527 4 v 446 1202 4 113 v 914 1202 V 965 1168 a(Bu\013er)31 b(10)p 1420 1202 V 142 w(62.2)109 b(\(14\))p 1951 1202 V 101 w(72.8)101 b(\(16\))p 2473 1202 V 102 w Fa(68.7)f Fg(\(15\))p 3020 1202 V 221 w(2s)p 3440 1202 V 916 1205 2527 4 v 446 1315 4 113 v 914 1315 V 965 1281 a(Bu\013er)31 b(21)p 1420 1315 V 142 w(67)179 b(\(15\))p 1951 1315 V 101 w(72.7)101 b(\(16\))p 2473 1315 V 102 w Fa(70.2)f Fg(\(15\))p 3020 1315 V 221 w(1s)p 3440 1315 V 448 1318 2994 4 v 446 1431 4 113 v 914 1431 V 965 1397 a(General)p 1420 1431 V 198 w(65.2)109 b(\(13\))p 1951 1431 V 101 w(71.5)101 b(\(14\))p 2473 1431 V 102 w Fa(69.7)f Fg(\(13\))p 3020 1431 V 221 w(1s)p 3440 1431 V 916 1435 2527 4 v 446 1544 4 113 v 914 1544 V 965 1510 a(La)m(y)m(er)32 b Fc(a)p 1420 1544 V 207 w Fg(64.9)109 b(\(13\))p 1951 1544 V 101 w(70.8)101 b(\(14\))p 2473 1544 V 102 w Fa(66.9)f Fg(\(13\))p 3020 1544 V 221 w(1s)p 3440 1544 V 916 1548 2527 4 v 446 1657 4 113 v 533 1623 a(27{28.5)p 914 1657 V 137 w(La)m(y)m(er)32 b Fc(b)p 1420 1657 V 216 w Fg(65.2)109 b(\(13\))p 1951 1657 V 101 w(71.1)101 b(\(14\))p 2473 1657 V 102 w Fa(68.6)f Fg(\(13\))p 3020 1657 V 221 w(2s)p 3440 1657 V 916 1660 2527 4 v 446 1770 4 113 v 914 1770 V 965 1736 a(Bu\013er)31 b(10)p 1420 1770 V 142 w(55.5)109 b(\(11\))p 1951 1770 V 101 w(70.7)101 b(\(14\))p 2473 1770 V 102 w Fa(64.1)f Fg(\(12\))p 3020 1770 V 221 w(2s)p 3440 1770 V 916 1773 2527 4 v 446 1883 4 113 v 914 1883 V 965 1849 a(Bu\013er)31 b(21)p 1420 1883 V 142 w(64.7)109 b(\(13\))p 1951 1883 V 101 w(71.1)101 b(\(14\))p 2473 1883 V 102 w Fa(68.1)f Fg(\(13\))p 3020 1883 V 221 w(1s)p 3440 1883 V 448 1886 2994 4 v 448 1889 V 1522 2061 a Fa(Medium)34 b(In)m(terv)-6 b(als)p 448 2172 3123 4 v 446 2285 4 113 v 498 2251 a Fg(Diameter)p 914 2285 V 1420 2285 V 1203 w(Occupancy)p 3148 2285 V 695 w(Av)m(erage)p 3569 2285 V 1422 2288 1729 4 v 446 2398 4 113 v 533 2364 a(in)m(terv)h(al)p 914 2398 V 965 2305 a(Algorithm)p 1420 2398 V 1491 2364 a(W)d(orst)31 b(case)p 1988 2398 V 170 w(Best)g(case)p 2556 2398 V 237 w(Av)m(erage)p 3148 2398 V 259 w(time)p 3569 2398 V 448 2401 3123 4 v 448 2418 V 446 2531 4 113 v 914 2531 V 965 2497 a(General)p 1420 2531 V 198 w(77.7)101 b(\(105\))p 1988 2531 V 102 w(78.5)g(\(111\))p 2556 2531 V 102 w Fa(78)181 b Fg(\(107\))p 3148 2531 V 222 w(3s)p 3569 2531 V 916 2534 2656 4 v 446 2643 4 113 v 914 2643 V 965 2610 a(La)m(y)m(er)32 b Fc(a)p 1420 2643 V 207 w Fg(72.8)147 b(\(97\))p 1988 2643 V 101 w(76.5)101 b(\(105\))p 2556 2643 V 102 w Fa(74.7)f Fg(\(102\))p 3148 2643 V 222 w(3s)p 3569 2643 V 916 2647 2656 4 v 446 2756 4 113 v 591 2722 a(9{12)p 914 2756 V 194 w(La)m(y)m(er)32 b Fc(b)p 1420 2756 V 216 w Fg(73)171 b(\(100\))p 1988 2756 V 102 w(76.8)101 b(\(110\))p 2556 2756 V 102 w Fa(74.7)f Fg(\(104\))p 3148 2756 V 222 w(5s)p 3569 2756 V 916 2760 2656 4 v 446 2869 4 113 v 914 2869 V 965 2835 a(Bu\013er)31 b(10)p 1420 2869 V 142 w(70.8)147 b(\(97\))p 1988 2869 V 101 w(76.4)101 b(\(106\))p 2556 2869 V 102 w Fa(74.7)f Fg(\(102\))p 3148 2869 V 222 w(7s)p 3569 2869 V 916 2873 2656 4 v 446 2982 4 113 v 914 2982 V 965 2948 a(Bu\013er)31 b(21)p 1420 2982 V 142 w(74.1)101 b(\(101\))p 1988 2982 V 102 w(76.8)g(\(106\))p 2556 2982 V 102 w Fa(75.5)f Fg(\(103\))p 3148 2982 V 222 w(3s)p 3569 2982 V 448 2986 3123 4 v 448 3002 V 446 3115 4 113 v 914 3115 V 965 3081 a(General)p 1420 3115 V 198 w(75.9)147 b(\(61\))p 1988 3115 V 101 w(78.6)g(\(66\))p 2556 3115 V 101 w Fa(77.5)f Fg(\(64\))p 3148 3115 V 221 w(3s)p 3569 3115 V 916 3118 2656 4 v 446 3228 4 113 v 914 3228 V 965 3194 a(La)m(y)m(er)32 b Fc(a)p 1420 3228 V 207 w Fg(73.5)147 b(\(61\))p 1988 3228 V 101 w(76.6)g(\(64\))p 2556 3228 V 101 w Fa(75.1)f Fg(\(62\))p 3148 3228 V 221 w(3s)p 3569 3228 V 916 3231 2656 4 v 446 3341 4 113 v 568 3307 a(12{15)p 914 3341 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 3341 V 216 w Fg(73.8)147 b(\(61\))p 1988 3341 V 101 w(76)217 b(\(64\))p 2556 3341 V 101 w Fa(74.9)146 b Fg(\(62\))p 3148 3341 V 221 w(4s)p 3569 3341 V 916 3344 2656 4 v 446 3454 4 113 v 914 3454 V 965 3420 a(Bu\013er)31 b(10)p 1420 3454 V 142 w(72.1)147 b(\(60\))p 1988 3454 V 101 w(76)217 b(\(64\))p 2556 3454 V 101 w Fa(73.7)146 b Fg(\(61\))p 3148 3454 V 221 w(5s)p 3569 3454 V 916 3457 2656 4 v 446 3567 4 113 v 914 3567 V 965 3533 a(Bu\013er)31 b(21)p 1420 3567 V 142 w(73.8)147 b(\(61\))p 1988 3567 V 101 w(77.4)g(\(63\))p 2556 3567 V 101 w Fa(75.3)f Fg(\(62\))p 3148 3567 V 221 w(1s)p 3569 3567 V 448 3570 3123 4 v 448 3587 V 446 3699 4 113 v 914 3699 V 965 3666 a(General)p 1420 3699 V 198 w(74.6)h(\(41\))p 1988 3699 V 101 w(76.8)g(\(44\))p 2556 3699 V 101 w Fa(75.5)f Fg(\(42\))p 3148 3699 V 221 w(1s)p 3569 3699 V 916 3703 2656 4 v 446 3812 4 113 v 914 3812 V 965 3779 a(La)m(y)m(er)32 b Fc(a)p 1420 3812 V 207 w Fg(71.5)147 b(\(39\))p 1988 3812 V 101 w(75.7)g(\(42\))p 2556 3812 V 101 w Fa(74.1)f Fg(\(41\))p 3148 3812 V 221 w(2s)p 3569 3812 V 916 3816 2656 4 v 446 3925 4 113 v 568 3891 a(15{18)p 914 3925 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 3925 V 216 w Fg(70.6)147 b(\(39\))p 1988 3925 V 101 w(76.5)g(\(43\))p 2556 3925 V 101 w Fa(73.9)f Fg(\(41\))p 3148 3925 V 221 w(2s)p 3569 3925 V 916 3929 2656 4 v 446 4038 4 113 v 914 4038 V 965 4004 a(Bu\013er)31 b(10)p 1420 4038 V 142 w(70.3)147 b(\(39\))p 1988 4038 V 101 w(76.8)g(\(43\))p 2556 4038 V 101 w Fa(73.8)f Fg(\(41\))p 3148 4038 V 221 w(3s)p 3569 4038 V 916 4042 2656 4 v 446 4151 4 113 v 914 4151 V 965 4117 a(Bu\013er)31 b(21)p 1420 4151 V 142 w(72.5)147 b(\(40\))p 1988 4151 V 101 w(76.7)g(\(42\))p 2556 4151 V 101 w Fa(74.7)f Fg(\(41\))p 3148 4151 V 221 w(1s)p 3569 4151 V 448 4154 3123 4 v 448 4171 V 446 4284 4 113 v 914 4284 V 965 4250 a(General)p 1420 4284 V 198 w(71.7)h(\(28\))p 1988 4284 V 101 w(76.1)g(\(31\))p 2556 4284 V 101 w Fa(73.9)f Fg(\(29\))p 3148 4284 V 221 w(1s)p 3569 4284 V 916 4287 2656 4 v 446 4397 4 113 v 914 4397 V 965 4363 a(La)m(y)m(er)32 b Fc(a)p 1420 4397 V 207 w Fg(69)217 b(\(27\))p 1988 4397 V 101 w(75)g(\(30\))p 2556 4397 V 101 w Fa(72.7)146 b Fg(\(29\))p 3148 4397 V 221 w(1s)p 3569 4397 V 916 4400 2656 4 v 446 4510 4 113 v 568 4476 a(18{21)p 914 4510 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 4510 V 216 w Fg(71.4)147 b(\(29\))p 1988 4510 V 101 w(74.1)g(\(30\))p 2556 4510 V 101 w Fa(72.5)f Fg(\(29\))p 3148 4510 V 221 w(2s)p 3569 4510 V 916 4513 2656 4 v 446 4623 4 113 v 914 4623 V 965 4589 a(Bu\013er)31 b(10)p 1420 4623 V 142 w(69.6)147 b(\(28\))p 1988 4623 V 101 w(73.9)g(\(30\))p 2556 4623 V 101 w Fa(71.8)f Fg(\(28\))p 3148 4623 V 221 w(2s)p 3569 4623 V 916 4626 2656 4 v 446 4736 4 113 v 914 4736 V 965 4702 a(Bu\013er)31 b(21)p 1420 4736 V 142 w(70.3)147 b(\(28\))p 1988 4736 V 101 w(75.4)g(\(30\))p 2556 4736 V 101 w Fa(72.8)f Fg(\(29\))p 3148 4736 V 221 w(2s)p 3569 4736 V 448 4739 3123 4 v 448 4756 V 446 4868 4 113 v 914 4868 V 965 4835 a(General)p 1420 4868 V 198 w(70.6)h(\(21\))p 1988 4868 V 101 w(76.5)g(\(24\))p 2556 4868 V 101 w Fa(73.6)f Fg(\(22\))p 3148 4868 V 221 w(1s)p 3569 4868 V 916 4872 2656 4 v 446 4981 4 113 v 914 4981 V 965 4947 a(La)m(y)m(er)32 b Fc(a)p 1420 4981 V 207 w Fg(67.4)147 b(\(21\))p 1988 4981 V 101 w(72.1)g(\(21\))p 2556 4981 V 101 w Fa(69.8)f Fg(\(21\))p 3148 4981 V 221 w(1s)p 3569 4981 V 916 4985 2656 4 v 446 5094 4 113 v 568 5060 a(21{24)p 914 5094 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 5094 V 216 w Fg(68.4)147 b(\(21\))p 1988 5094 V 101 w(73.8)g(\(23\))p 2556 5094 V 101 w Fa(71)227 b Fg(\(21\))p 3148 5094 V 221 w(1s)p 3569 5094 V 916 5098 2656 4 v 446 5207 4 113 v 914 5207 V 965 5173 a(Bu\013er)31 b(10)p 1420 5207 V 142 w(66.7)147 b(\(20\))p 1988 5207 V 101 w(74.3)g(\(22\))p 2556 5207 V 101 w Fa(70.9)f Fg(\(21\))p 3148 5207 V 221 w(1s)p 3569 5207 V 916 5210 2656 4 v 446 5320 4 113 v 914 5320 V 965 5286 a(Bu\013er)31 b(21)p 1420 5320 V 142 w(68.5)147 b(\(20\))p 1988 5320 V 101 w(73.8)g(\(22\))p 2556 5320 V 101 w Fa(71.5)f Fg(\(21\))p 3148 5320 V 221 w(2s)p 3569 5320 V 448 5323 3123 4 v Black 1897 5698 a(14)p Black eop %%Page: 15 15 15 14 bop Black Black 448 485 2994 4 v 446 598 4 113 v 498 564 a Fg(Diameter)p 914 598 V 1420 598 V 1138 w(Occupancy)p 3020 598 V 631 w(Av)m(erage)p 3440 598 V 1422 601 1600 4 v 446 711 4 113 v 533 677 a(in)m(terv)-5 b(al)p 914 711 V 965 618 a(Algorithm)p 1420 711 V 1472 677 a(W)d(orst)31 b(case)p 1951 711 V 128 w(Best)h(case)p 2473 711 V 191 w(Av)m(erage)p 3020 711 V 236 w(time)p 3440 711 V 448 714 2994 4 v 448 731 V 448 734 V 446 847 4 113 v 914 847 V 965 813 a(General)p 1420 847 V 198 w(68.6)109 b(\(16\))p 1951 847 V 101 w(74.1)101 b(\(17\))p 2473 847 V 102 w Fa(71.5)f Fg(\(16\))p 3020 847 V 221 w(1s)p 3440 847 V 916 850 2527 4 v 446 960 4 113 v 914 960 V 965 926 a(La)m(y)m(er)32 b Fc(a)p 1420 960 V 207 w Fg(67.4)109 b(\(16\))p 1951 960 V 101 w(73.2)101 b(\(17\))p 2473 960 V 102 w Fa(70.4)f Fg(\(16\))p 3020 960 V 221 w(1s)p 3440 960 V 916 963 2527 4 v 446 1073 4 113 v 568 1039 a(24{27)p 914 1073 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 1073 V 216 w Fg(67.5)109 b(\(16\))p 1951 1073 V 101 w(73.1)101 b(\(18\))p 2473 1073 V 102 w Fa(70.5)f Fg(\(16\))p 3020 1073 V 221 w(2s)p 3440 1073 V 916 1076 2527 4 v 446 1186 4 113 v 914 1186 V 965 1152 a(Bu\013er)31 b(10)p 1420 1186 V 142 w(63.4)109 b(\(15\))p 1951 1186 V 101 w(74.2)101 b(\(18\))p 2473 1186 V 102 w Fa(69.7)f Fg(\(16\))p 3020 1186 V 221 w(2s)p 3440 1186 V 916 1189 2527 4 v 446 1298 4 113 v 914 1298 V 965 1265 a(Bu\013er)31 b(21)p 1420 1298 V 142 w(66.6)109 b(\(16\))p 1951 1298 V 101 w(73)171 b(\(17\))p 2473 1298 V 102 w Fa(70)181 b Fg(\(16\))p 3020 1298 V 221 w(1s)p 3440 1298 V 448 1302 2994 4 v 448 1318 V 446 1431 4 113 v 914 1431 V 965 1397 a(General)p 1420 1431 V 198 w(64)e(\(12\))p 1951 1431 V 101 w(73.3)101 b(\(14\))p 2473 1431 V 102 w Fa(68.3)f Fg(\(12\))p 3020 1431 V 221 w(1s)p 3440 1431 V 916 1435 2527 4 v 446 1544 4 113 v 914 1544 V 965 1510 a(La)m(y)m(er)32 b Fc(a)p 1420 1544 V 207 w Fg(59.5)109 b(\(11\))p 1951 1544 V 101 w(70.8)101 b(\(13\))p 2473 1544 V 102 w Fa(67.7)f Fg(\(12\))p 3020 1544 V 221 w(1s)p 3440 1544 V 916 1548 2527 4 v 446 1657 4 113 v 568 1623 a(27{30)p 914 1657 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 1657 V 216 w Fg(64.8)109 b(\(12\))p 1951 1657 V 101 w(70.5)101 b(\(13\))p 2473 1657 V 102 w Fa(68.4)f Fg(\(12\))p 3020 1657 V 221 w(1s)p 3440 1657 V 916 1660 2527 4 v 446 1770 4 113 v 914 1770 V 965 1736 a(Bu\013er)31 b(10)p 1420 1770 V 142 w(57.2)109 b(\(11\))p 1951 1770 V 101 w(68.9)101 b(\(13\))p 2473 1770 V 102 w Fa(61.4)f Fg(\(11\))p 3020 1770 V 221 w(1s)p 3440 1770 V 916 1773 2527 4 v 446 1883 4 113 v 914 1883 V 965 1849 a(Bu\013er)31 b(21)p 1420 1883 V 142 w(57.5)109 b(\(11\))p 1951 1883 V 101 w(70)171 b(\(13\))p 2473 1883 V 102 w Fa(66.5)100 b Fg(\(12\))p 3020 1883 V 221 w(1s)p 3440 1883 V 448 1886 2994 4 v 448 1903 V 448 1906 V 1604 2077 a Fa(Large)34 b(in)m(terv)-6 b(als)p 448 2206 V 446 2319 4 113 v 498 2285 a Fg(Diameter)p 914 2319 V 1420 2319 V 1138 w(Occupancy)p 3020 2319 V 631 w(Av)m(erage)p 3440 2319 V 1422 2322 1600 4 v 446 2432 4 113 v 533 2398 a(in)m(terv)h(al)p 914 2432 V 965 2339 a(Algorithm)p 1420 2432 V 1472 2398 a(W)d(orst)31 b(case)p 1951 2432 V 128 w(Best)h(case)p 2473 2432 V 191 w(Av)m(erage)p 3020 2432 V 236 w(time)p 3440 2432 V 448 2435 2994 4 v 448 2452 V 446 2565 4 113 v 914 2565 V 965 2531 a(General)p 1420 2565 V 198 w(75.6)109 b(\(52\))p 1951 2565 V 101 w(78.4)101 b(\(63\))p 2473 2565 V 102 w Fa(77)181 b Fg(\(57\))p 3020 2565 V 221 w(3s)p 3440 2565 V 916 2568 2527 4 v 446 2678 4 113 v 914 2678 V 965 2644 a(La)m(y)m(er)32 b Fc(a)p 1420 2678 V 207 w Fg(71.8)109 b(\(49\))p 1951 2678 V 101 w(77.3)101 b(\(62\))p 2473 2678 V 102 w Fa(74.6)f Fg(\(56\))p 3020 2678 V 221 w(3s)p 3440 2678 V 916 2681 2527 4 v 446 2791 4 113 v 591 2757 a(9{19)p 914 2791 V 194 w(La)m(y)m(er)32 b Fc(b)p 1420 2791 V 216 w Fg(72.4)109 b(\(50\))p 1951 2791 V 101 w(77.4)101 b(\(61\))p 2473 2791 V 102 w Fa(74.9)f Fg(\(56\))p 3020 2791 V 221 w(4s)p 3440 2791 V 916 2794 2527 4 v 446 2904 4 113 v 914 2904 V 965 2870 a(Bu\013er)31 b(10)p 1420 2904 V 142 w(72.9)109 b(\(50\))p 1951 2904 V 101 w(76.4)101 b(\(63\))p 2473 2904 V 102 w Fa(74.6)f Fg(\(56\))p 3020 2904 V 221 w(5s)p 3440 2904 V 916 2907 2527 4 v 446 3016 4 113 v 914 3016 V 965 2983 a(Bu\013er)31 b(21)p 1420 3016 V 142 w(73.2)109 b(\(51\))p 1951 3016 V 101 w(77.4)101 b(\(64\))p 2473 3016 V 102 w Fa(75.8)f Fg(\(56\))p 3020 3016 V 221 w(2s)p 3440 3016 V 448 3020 2994 4 v 448 3036 V 446 3149 4 113 v 914 3149 V 965 3115 a(General)p 1420 3149 V 198 w(66.8)109 b(\(17\))p 1951 3149 V 101 w(75.9)101 b(\(22\))p 2473 3149 V 102 w Fa(71.7)f Fg(\(18\))p 3020 3149 V 221 w(1s)p 3440 3149 V 916 3153 2527 4 v 446 3262 4 113 v 914 3262 V 965 3228 a(La)m(y)m(er)32 b Fc(a)p 1420 3262 V 207 w Fg(67)179 b(\(17\))p 1951 3262 V 101 w(75.3)101 b(\(21\))p 2473 3262 V 102 w Fa(71.6)f Fg(\(18\))p 3020 3262 V 221 w(1s)p 3440 3262 V 916 3266 2527 4 v 446 3375 4 113 v 568 3341 a(19{29)p 914 3375 V 172 w(La)m(y)m(er)32 b Fc(b)p 1420 3375 V 216 w Fg(66.8)109 b(\(16\))p 1951 3375 V 101 w(74.5)101 b(\(20\))p 2473 3375 V 102 w Fa(71.1)f Fg(\(18\))p 3020 3375 V 221 w(2s)p 3440 3375 V 916 3378 2527 4 v 446 3488 4 113 v 914 3488 V 965 3454 a(Bu\013er)31 b(10)p 1420 3488 V 142 w(65.3)109 b(\(17\))p 1951 3488 V 101 w(73.6)101 b(\(24\))p 2473 3488 V 102 w Fa(70.6)f Fg(\(18\))p 3020 3488 V 221 w(2s)p 3440 3488 V 916 3491 2527 4 v 446 3601 4 113 v 914 3601 V 965 3567 a(Bu\013er)31 b(21)p 1420 3601 V 142 w(68.5)109 b(\(16\))p 1951 3601 V 101 w(74.8)101 b(\(21\))p 2473 3601 V 102 w Fa(71.2)f Fg(\(18\))p 3020 3601 V 221 w(1s)p 3440 3601 V 448 3604 2994 4 v 448 3621 V 446 3734 4 113 v 914 3734 V 965 3700 a(General)p 1420 3734 V 198 w(71.1)109 b(\(25\))p 1951 3734 V 101 w(77.6)101 b(\(38\))p 2473 3734 V 102 w Fa(74.8)f Fg(\(29\))p 3020 3734 V 221 w(1s)p 3440 3734 V 916 3737 2527 4 v 446 3847 4 113 v 914 3847 V 965 3813 a(La)m(y)m(er)32 b Fc(a)p 1420 3847 V 207 w Fg(63.6)109 b(\(21\))p 1951 3847 V 101 w(74.4)101 b(\(36\))p 2473 3847 V 102 w Fa(70.4)f Fg(\(27\))p 3020 3847 V 221 w(1s)p 3440 3847 V 916 3850 2527 4 v 446 3960 4 113 v 591 3926 a(9{29)p 914 3960 V 194 w(La)m(y)m(er)32 b Fc(b)p 1420 3960 V 216 w Fg(69.3)109 b(\(21\))p 1951 3960 V 101 w(74.6)101 b(\(34\))p 2473 3960 V 102 w Fa(72.6)f Fg(\(27\))p 3020 3960 V 221 w(2s)p 3440 3960 V 916 3963 2527 4 v 446 4073 4 113 v 914 4073 V 965 4039 a(Bu\013er)31 b(10)p 1420 4073 V 142 w(61.6)109 b(\(25\))p 1951 4073 V 101 w(77)171 b(\(33\))p 2473 4073 V 102 w Fa(71.2)100 b Fg(\(29\))p 3020 4073 V 221 w(2s)p 3440 4073 V 916 4076 2527 4 v 446 4185 4 113 v 914 4185 V 965 4152 a(Bu\013er)31 b(21)p 1420 4185 V 142 w(71.9)109 b(\(24\))p 1951 4185 V 101 w(77.5)101 b(\(35\))p 2473 4185 V 102 w Fa(74.6)f Fg(\(28\))p 3020 4185 V 221 w(4s)p 3440 4185 V 448 4189 2994 4 v 448 4192 V Black 1897 5698 a(15)p Black eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF