%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: manual.dvi %%Pages: 29 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%DocumentFonts: Helvetica-Bold MTSYN AvantGarde-Demi Helvetica %%+ Times-Roman Times-Bold RMTMI Times-Italic Helvetica-Narrow-Bold %%+ Helvetica-Narrow Times-BoldItalic Courier MTEX %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o manual.ps manual %DVIPSParameters: dpi=1200, compressed %DVIPSSource: TeX output 2003.08.15:1401 %%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 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{ rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{ /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{ A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse} ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{ 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop} forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 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: psfrag.pro %% %% This is file `psfrag.pro', %% generated with the docstrip utility. %% %% The original source files were: %% %% psfrag.dtx (with options: `filepro') %% %% Copyright (c) 1996 Craig Barratt, Michael C. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MTEX %!PS-AdobeFont-1.1: MTEX 1.1 %%CreationDate: 1993 Jun 26 10:30:36 % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation) readonly def /FullName (MTEX) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /MTEX def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 80 /summationtext put readonly def /FontBBox{-23 -2958 1456 766}readonly def /UniqueXX 5018948 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311d70c1e2528f01045f8caec9829f31d6 48c8d0a29ea851af41c327a0d569abaafe5afe94dad818c312d3cee72f1acea0 b701b6a5608521a2866790bdd5776d6cd0c7d971b9a48b96aa970dcbb8b76edc b90da356dc2529b665eb4bb80ac4f5b0f4c0ed76861e399638ad3db1be4759c7 8d4f2e81a2ff688d366b91d729d63ab5fc9556fe10a07b81904d879a7446da82 dc107ff41b0e3b7c2245d57b2ee9bab31eccfe9b79e3ec32cb1f10c622f4bce1 8df0e5c4b98ec714593d6f127c5cf6d719a79b83c627433d3aa39cb88ef85d27 4184c4b4c46ca5b496f20460ed75ccfb3d66073b710cc1ad2f2bec4ac64065ed 5e03930ed9ec97810f36845dd5048d90d724a88fd3c814ce17c417c84ba45c43 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: MTSYN %!PS-AdobeFont-1.1: MTSYN 1.000 %%CreationDate: 1996 Aug 26 20:27:17 % MathTime fonts were designed by Michael Spivak. % Copyright (c) 1996 Publish or Perish, Inc. % Hinting Copyright (c) 1996 Y&Y, Inc. % MathTime is a registered trademark of Publish or Perish, Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.000) readonly def /Notice (Copyright (c) 1992-1996 Publish or Perish and Y&Y, Inc.) readonly def /FullName (MTSYN) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /MTSYN def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 2 /multiply put dup 3 /asteriskmath put dup 15 /bullet put dup 67 /plus put dup 68 /equal put dup 102 /braceleft put dup 103 /braceright put readonly def /FontBBox{0 -954 1043 900}readonly def /UniqueID 5087393 def currentdict end currentfile eexec 80347982ab3942d930e069a70d0d48311e252234d51741e18db3a68e8ad10242 29e5817a10e796a78d2c7f7c1f50961b9a57aa604c9f821dbf5a9295197bc666 31678d7d2c7e1f8f2151ce0c29efce46270570f4301c5dad1b38884732e53dad 05dfc36b020e726ca575f71f04abf2b49e1f1d6d2a08a477658ca9a48f1c8cce 14382f0a42201de56e2821ee2b0e91a818b1b753d810ec2428dae5153b66af66 a6cbcba4db2bf926e909644db41326e327493b2750168d128a100fe56c76b17c 16f9ce939588d19c6e9cda7cb062196e66e38e537670953934ffc63663c7146a 12277d8f7c13b563981d696e0abe4478eabeba753024ebdf3ee17f2613df08c9 228159906a48ddeed6212332ef96023e5c73ea55aac6a2b938138ec26b4732c1 1e8fed889257e9d4f2002935585d9aa2265929948e37bab7adf12f1a22b3c68d 09a6b6c4e14b1470ecf0874d92d964cfbb8e2a0e4cbd1a114cc05bbdee4699a5 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6346 7110 l cp gs 0.00 setgray ef gr col-1 s % Polyline 7.500 slw gs clippath 6615 8910 m 6615 8790 l 6346 8790 l 6526 8850 l 6346 8910 l cp eoclip n 5700 8850 m 6600 8850 l gs col7 1.00 shd ef gr gs col-1 s gr gr % arrowhead 45.000 slw n 6346 8910 m 6526 8850 l 6346 8790 l 6346 8910 l cp gs 0.00 setgray ef gr col-1 s % Polyline 7.500 slw gs clippath 6615 10710 m 6615 10590 l 6346 10590 l 6526 10650 l 6346 10710 l cp eoclip n 5700 10650 m 6600 10650 l gs col7 1.00 shd ef gr gs col-1 s gr gr % arrowhead 45.000 slw n 6346 10710 m 6526 10650 l 6346 10590 l 6346 10710 l cp gs 0.00 setgray ef gr col-1 s % Polyline 7.500 slw gs clippath 6615 12510 m 6615 12390 l 6346 12390 l 6526 12450 l 6346 12510 l cp eoclip n 5700 12450 m 6600 12450 l gs col7 1.00 shd ef gr gs col-1 s gr gr % arrowhead 45.000 slw n 6346 12510 m 6526 12450 l 6346 12390 l 6346 12510 l cp gs 0.00 setgray ef gr col-1 s % Polyline 7.500 slw gs clippath 11092 3811 m 11135 3699 l 10882 3604 l 11030 3724 l 10840 3716 l cp eoclip 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clippath 16506 3211 m 16523 3092 l 16256 3054 l 16426 3139 l 16239 3172 l cp eoclip n 14400 2850 m 16500 3150 l gs col7 1.00 shd ef gr gs col-1 s gr gr % arrowhead 45.000 slw n 16239 3172 m 16426 3139 l 16256 3054 l 16239 3172 l cp gs 0.00 setgray ef gr col-1 s % Polyline 7.500 slw gs clippath 11137 2523 m 11089 2414 l 10843 2522 l 11032 2505 l 10891 2632 l cp eoclip n 9900 3000 m 11100 2475 l gs col7 1.00 shd ef gr gs col-1 s gr gr % arrowhead 45.000 slw n 10891 2632 m 11032 2505 l 10843 2522 l 10891 2632 l cp gs 0.00 setgray ef gr col-1 s % Polyline 7.500 slw n 2505 2700 m 2400 2700 2400 3495 105 arcto 4 {pop} repeat 2400 3600 5595 3600 105 arcto 4 {pop} repeat 5700 3600 5700 2805 105 arcto 4 {pop} repeat 5700 2700 2505 2700 105 arcto 4 {pop} repeat cp gs col7 1.00 shd ef gr gs col-1 s gr % Polyline n 2505 4800 m 2400 4800 2400 5595 105 arcto 4 {pop} repeat 2400 5700 5595 5700 105 arcto 4 {pop} repeat 5700 5700 5700 4905 105 arcto 4 {pop} repeat 5700 4800 2505 4800 105 arcto 4 {pop} repeat cp gs col7 1.00 shd ef gr gs col-1 s gr % Polyline n 6705 2700 m 6600 2700 6600 3495 105 arcto 4 {pop} repeat 6600 3600 9795 3600 105 arcto 4 {pop} repeat 9900 3600 9900 2805 105 arcto 4 {pop} repeat 9900 2700 6705 2700 105 arcto 4 {pop} repeat cp gs col7 1.00 shd ef gr gs col-1 s gr % Polyline n 11205 3300 m 11100 3300 11100 4095 105 arcto 4 {pop} repeat 11100 4200 14295 4200 105 arcto 4 {pop} repeat 14400 4200 14400 3405 105 arcto 4 {pop} repeat 14400 3300 11205 3300 105 arcto 4 {pop} repeat cp gs col7 0.90 shd ef gr gs col-1 s gr % Polyline n 11205 2100 m 11100 2100 11100 2895 105 arcto 4 {pop} repeat 11100 3000 14295 3000 105 arcto 4 {pop} repeat 14400 3000 14400 2205 105 arcto 4 {pop} repeat 14400 2100 11205 2100 105 arcto 4 {pop} repeat cp gs col7 1.00 shd ef gr gs col-1 s gr /Helvetica-iso ff 240.00 scf sf 10425 2625 m gs 1 -1 sc 20.0 rot (YES) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 210.00 scf sf 10500 3900 m gs 1 -1 sc 340.0 rot (YES or NO) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 15225 1950 m gs 1 -1 sc 8.0 rot (High quality) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 15375 2850 m gs 1 -1 sc 352.0 rot (Low quality) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold-iso ff 240.00 scf sf 8700 12525 m gs 1 -1 sc (ParMETIS_V3_NodeND) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold-iso ff 240.00 scf sf 8700 10800 m gs 1 -1 sc (ParMETIS_V3_RefineKway) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold-iso ff 240.00 scf sf 8700 9000 m gs 1 -1 sc (ParMETIS_V3_AdaptiveRepart) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold-iso ff 240.00 scf sf 8700 7200 m gs 1 -1 sc (ParMETIS_V3_Mesh2Dual) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold-iso ff 240.00 scf sf 8700 5400 m gs 1 -1 sc (ParMETIS_V3_PartMeshKway) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold-iso ff 240.00 scf sf 12750 3900 m gs 1 -1 sc (ParMETIS_V3_PartKway) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold-iso ff 240.00 scf sf 18262 2100 m gs 1 -1 sc (ParMETIS_V3_PartGeomKway) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold-iso ff 240.00 scf sf 18300 3225 m gs 1 -1 sc (ParMETIS_V3_PartGeom) dup sw pop 2 div neg 0 rm col-1 sh gr % Polyline n 780 4425 m 675 4425 675 11520 105 arcto 4 {pop} repeat 675 11625 1170 11625 105 arcto 4 {pop} repeat 1275 11625 1275 4530 105 arcto 4 {pop} repeat 1275 4425 780 4425 105 arcto 4 {pop} repeat cp gs col7 1.00 shd ef gr gs col-1 s gr /Helvetica-iso ff 360.00 scf sf 1125 8025 m gs 1 -1 sc 90.0 rot (ParMetis Can Do The Following) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 4050 3225 m gs 1 -1 sc (Partition a graph) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 4050 5325 m gs 1 -1 sc (Partition a mesh) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 4050 10575 m gs 1 -1 sc (Refine the quality) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 4050 10875 m gs 1 -1 sc (of a partitioning) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 4050 12375 m gs 1 -1 sc (Compute a fill-reducing ) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 4050 12675 m gs 1 -1 sc (ordering) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 8250 3405 m gs 1 -1 sc (for the vertices?) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 8250 3075 m gs 1 -1 sc (Do you have coordinates) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 12750 2475 m gs 1 -1 sc (What are your ) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 240.00 scf sf 12750 2805 m gs 1 -1 sc (time/quality tradeoffs?) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 210.00 scf sf 4050 8775 m gs 1 -1 sc (Repartition a graph corresponding) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-iso ff 210.00 scf sf 4050 9075 m gs 1 -1 sc (to an adaptively refined mesh) dup sw pop 2 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6523.9 7057.0 6524.9 7099 6517 curveto 7115.9 6513.8 7138.4 6505.1 7189 6482 curveto gs col2 s gr gr % Interp Spline gs n 6704 6688 m 6821.3 6688.0 6871.9 6689.9 6906 6696 curveto 6932.3 6700.3 6967.8 6711.6 7049 6741 curveto gs col2 s gr gr /Times-Roman ff 150.00 scf sf 6204 6752 m gs 1 -1 sc (3) col-1 sh gr /Times-Italic ff 240.00 scf sf 6024 6707 m gs 1 -1 sc (G) col-1 sh gr /Times-Italic ff 240.00 scf sf 2745 3690 m gs 1 -1 sc (G) col-1 sh gr % Interp Spline gs n 5414 7347 m 5498.1 7392.1 5535.6 7409.6 5564 7417 curveto 5595.0 7425.1 5667.3 7429.7 5699 7427 curveto 5709.9 7426.1 5724.9 7422.3 5759 7412 curveto gs col2 s gr gr % Interp Spline gs n 6784 5287 m 6961.1 5277.3 7037.6 5268.3 7090 5251 curveto 7143.4 5233.4 7256.4 5188.6 7294 5134 curveto 7334.0 5076.0 7343.5 4950.1 7333 4887 curveto 7329.2 4863.9 7314.9 4836.9 7276 4779 curveto gs col2 s gr gr % Interp Spline gs n 7251 5187 m 7301.1 5309.2 7320.6 5362.9 7329 5402 curveto 7338.6 5446.5 7346.2 5551.6 7344 5597 curveto 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1572 curveto 8523.3 1475.5 8539.3 1264.2 8522 1158 curveto 8515.2 1119.3 8491.3 1074.0 8426 976 curveto gs col2 s gr gr % Interp Spline gs n 8384 1662 m 8468.1 1867.2 8500.8 1957.5 8514 2023 curveto 8531.1 2097.9 8543.9 2274.4 8541 2350 curveto 8538.9 2375.8 8532.6 2411.5 8514 2493 curveto gs col2 s gr gr % Interp Spline gs n 8507 1460 m 8844.8 1555.1 8993.5 1587.8 9102 1591 curveto 9206.7 1594.2 9439.5 1560.8 9539 1523 curveto 9578.7 1507.2 9628.5 1474.5 9738 1392 curveto gs col2 s gr gr % Interp Spline gs n 8523 2081 m 8834.7 2028.2 8971.2 2013.5 9069 2023 curveto 9133.7 2029.4 9219.8 2056.3 9414 2130 curveto gs col2 s gr gr % Interp Spline gs n 6618 4993 m 6730.0 5152.6 6772.7 5226.1 6789 5287 curveto 6802.4 5337.1 6803.0 5446.7 6788 5497 curveto 6779.7 5524.8 6758.7 5557.3 6704 5627 curveto gs col2 s gr gr /Times-Roman ff 150.00 scf sf 7240 1978 m gs 1 -1 sc (O) col-1 sh gr /Times-Roman ff 150.00 scf sf 6864 3882 m gs 1 -1 sc (1) col-1 sh gr /Times-Italic ff 240.00 scf sf 6684 3837 m gs 1 -1 sc (G) col-1 sh gr /Times-Roman ff 150.00 scf sf 6609 5442 m gs 1 -1 sc (2) col-1 sh gr /Times-Italic ff 240.00 scf sf 6429 5397 m gs 1 -1 sc (G) col-1 sh gr 7.500 slw % Arc gs clippath 3523 7341 m 3649 7416 l 3504 7398 l 3679 7458 l 3699 7402 l cp clip n 4758.3 4091.7 3505.0 -155.3 108.0 arcn gs col-1 s gr gr % arrowhead n 3523 7341 m 3649 7416 l 3504 7398 l 3536 7377 l 3523 7341 l cp gs 0.00 setgray ef gr col-1 s % Arc gs clippath 9389 3098 m 9381 2951 l 9447 3083 l 9400 2903 l 9342 2918 l cp clip n 5725.6 3971.0 3796.4 68.4 -16.0 arcn gs col-1 s gr gr % arrowhead n 9389 3098 m 9381 2951 l 9447 3083 l 9412 3067 l 9389 3098 l cp gs 0.00 setgray ef gr col-1 s /Helvetica-Bold ff 210.00 scf sf 1050 4200 m gs 1 -1 sc 90.0 rot (Coarsening Phase) dup sw pop 2 div neg 0 rm col4 sh gr /Helvetica-Bold ff 210.00 scf sf 9750 4200 m gs 1 -1 sc 270.0 rot (Uncoarsening Phase) dup sw pop 2 div neg 0 rm col4 sh gr /Helvetica-Bold ff 210.00 scf sf 5400 8025 m gs 1 -1 sc (Initial Partitioning Phase) dup sw pop 2 div neg 0 rm col4 sh gr /Helvetica-Bold ff 240.00 scf sf 5400 525 m gs 1 -1 sc (Multilevel K-way Partitioning) dup sw pop 2 div neg 0 rm col1 sh gr $F2psEnd rs %%EndDocument @endspecial 0 3963 a Fx(Figure)43 b(2)p FK(:)108 b Fv(The)34 b(three)f(phases)h(of)g(m)o(ultile)m(v)m(el)h Fn(k)8 b Fv(-w)o(a)m(y)33 b(g)o(r)o(aph)g(par)t(titioning.)50 b(Dur)r(ing)32 b(the)i(coarsening)f(phase)o(,)h(the)g(siz)o(e)h(of)f (the)g(g)o(r)o(aph)f(is)i(successiv)m(ely)i(decreased.)49 b(Dur)r(ing)33 b(the)0 4162 y(initial)e(par)t(titioning)e(phase)o(,)g (a)h Fn(k)8 b Fv(-w)o(a)m(y)30 b(par)t(titioning)g(is)h(computed,)e (Dur)r(ing)g(the)h(m)o(ultile)m(v)m(el)g(re\002nement)f(\(or)i (uncoarsening\))e(phase)o(,)g(the)h(par)t(titioning)f(is)i(successiv)m (ely)i(re\002ned)d(as)g(it)h(is)0 4362 y(projected)e(to)h(the)g(larger) g(g)o(r)o(aphs)o(.)39 b Fn(G)1594 4390 y Fq(0)1689 4362 y Fv(is)31 b(the)f(input)g(g)o(r)o(aph,)f(which)g(is)i(the)f(\002nest)h (g)o(r)o(aph.)39 b Fn(G)3924 4390 y Fl(i)12 b FI(C)p Fq(1)4150 4362 y Fv(is)31 b(the)f(ne)m(xt)g(le)m(v)m(el)g(coarser)g(g)o (r)o(aph)f(of)34 b Fn(G)5850 4389 y Fl(i)5900 4362 y Fv(.)41 b Fn(G)6075 4390 y Fq(4)6170 4362 y Fv(is)31 b(the)f(coarsest)h(g)o(r)o(aph.)0 4731 y FK(adjacent)50 b(v)n(ertices)g(of)h(the)g(input)g(graph)g(in)g(order)h(to)f(form)h(a)e (related)h(coarser)f(graph.)79 b(Computation)52 b(of)f(the)g(initial)g (partitioning)0 4950 y(is)46 b(performed)g(on)g(the)g(coarsest)f(\(and) h(hence)f(smallest\))g(of)h(these)g(graphs,)g(and)f(so)h(is)g(v)n(ery)f (f)n(ast.)64 b(Finally)-11 b(,)48 b(partition)e(re\002nement)g(is)0 5170 y(performed)54 b(on)f(each)f(le)l(v)n(el)g(graph,)k(from)e(the)f (coarsest)f(to)h(the)g(\002nest)g(\()p Fs(i.e)o FK(.,)i(original)f (graph\))f(using)g(a)g(KL/FM-type)h(re\002nement)0 5389 y(algorithm)42 b([2)q(,)f(9].)51 b(Figure)42 b(2)f(illustrates)h(the)f (multile)l(v)n(el)g(graph)h(partitioning)g(paradigm.)199 5608 y(Comparisons)58 b(performed)g(in)h([7])f(ha)m(v)n(e)f(sho)l(wn)g (that)h(serial)g(multile)l(v)n(el)g Fy(k)10 b FK(-w)n(ay)58 b(partitioning)h(is)f(o)n(v)n(er)f(50)h(times)g(f)n(aster)g(than)0 5827 y(multile)l(v)n(el)39 b(spectral)g(bisection)g([12])h(while)g (producing)f(partitionings)h(that)g(cut)f(10\045)h(to)f(50\045)h(fe)l (wer)f(edges.)50 b(Our)39 b(e)n(xperiments)g(on)0 6046 y(a)j(1024-processor)g(Cray)g(T3E)h(ha)m(v)n(e)e(sho)l(wn)h(that)h FA(P)-7 b(arMETIS)p 3757 6046 50 7 v 61 w(V3)p 4021 6046 V 59 w(P)g(ar)7 b(tKw)n(a)-5 b(y)43 b FK(can)f(partition)h(a)f (500-million)h(element)f(3D)g(mesh)0 6265 y(in)g(well)f(under)h(a)f (minute!)199 6485 y(Recall)d(that)g(we)f(mentioned)i(that)f(if)g(the)g (graph)g(is)g(well)g(distrib)m(uted)g(among)g(the)g(processors)f FA(P)-7 b(arMETIS)p 6459 6485 V 61 w(V3)p 6723 6485 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)38 b FK(runs)0 6704 y(f)n(aster)-9 b(.)79 b(In)51 b(f)n(act,)i(our)e(e)n(xperiments)f(ha)m(v)n(e)f(sho)l (wn)h(that)h(when)g(we)f(use)g FA(P)-7 b(arMETIS)p 4975 6704 V 61 w(V3)p 5239 6704 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)51 b FK(to)g(partition)g(a)g(graph)f(that)h(is)0 6923 y(distrib)m(uted)57 b(according)f(to)h(the)g(partitioning)h (produced)f(by)g(an)f(earlier)h(call)g(to)g FA(P)-7 b(arMETIS)p 5596 6923 V 61 w(V3)p 5860 6923 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)p FK(,)6715 6863 y Fr(2)6847 6923 y FK(the)57 b(amount)g(of)0 7142 y(time)40 b(required)f(for)h(this)g(second)e(partitioning)j(is)e (often)g(reduced)g(by)h(a)f(f)n(actor)h(of)g(tw)n(o)g(to)f(four)-9 b(.)51 b(The)40 b(reason)f(for)h(this)f(has)g(to)g(do)h(with)0 7361 y(the)f(inter)m(-processor)g(communication)h(pattern)f(of)h FA(P)-7 b(arMETIS)p 3793 7361 V 61 w(V3)p 4057 7361 V 59 w(P)g(ar)7 b(tKw)n(a)-5 b(y)p FK(.)51 b(If)40 b(the)f(graph)g(is)g (initially)h(distrib)m(uted)g(randomly)0 7581 y(\()p Fs(i.e)p FK(.,)51 b(there)f(are)g(man)n(y)g(interf)n(ace)g(v)n (ertices\),)h(each)e(processor)h(spends)f(a)h(lot)g(of)h(time)f (communicating)g(information)i(about)e(these)0 7800 y(interf)n(ace)g(v) n(ertices)f(to)i(man)n(y)e(other)i(processors.)75 b(On)50 b(the)g(other)h(hand,)g(if)g(the)f(graph)g(is)g(well)g(distrib)m(uted,) i(the)e(number)g(of)h(inter)m(-)0 8019 y(f)n(ace)c(v)n(ertices)g(is)g (much)g(smaller)h(\(as)f(is)g(the)h(number)f(of)h(other)g(processors)e (with)i(whom)g(each)e(processor)h(has)g(to)h(communicate\),)0 8238 y(reducing)f(the)f(o)n(v)n(erall)g(runtime)h(of)g(the)g (partitioner)-9 b(.)67 b(Of)47 b(course,)f(this)h(is)f(the)h(chick)n (en)f(and)h(e)n(gg)f(problem.)67 b(Ho)l(w)46 b(can)g(we)g(initially)0 8457 y(distrib)m(ute)53 b(the)g(graph)f(nicely)h(without)g(ha)m(ving)g (\002rst)g(partitioned)g(it?)86 b(W)-13 b(e)52 b(ha)m(v)n(e)f(de)l(v)n (eloped)h(one)h(such)f(method)h(for)g(partitioning)0 8676 y(graphs)h(that)g(correspond)f(to)i(\002nite)f(element)g(meshes.) 87 b(This)54 b(is)g(to)g(quickly)g(compute)g(a)g(f)n(airly)h(good)f (initial)g(partitioning)h(using)0 8896 y(the)d(coordinate)f(v)l(alues)g (of)h(the)g(mesh.)82 b(W)-13 b(e)51 b(can)g(then)h(redistrib)m(ute)f (the)h(graph)g(according)g(to)g(this)f(initial)i(partitioning)f(and)g (then)0 9115 y(call)46 b FA(P)-7 b(arMETIS)p 1054 9115 V 60 w(V3)p 1317 9115 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)46 b FK(on)g(the)g(redistrib)m(uted)f(graph.)68 b FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)52 b FK(pro)n(vides)45 b(the)h FA(P)-7 b(arMETIS)p 6331 9115 V 61 w(V3)p 6595 9115 V 60 w(P)g(ar)7 b(tGeomKw)n(a)-5 b(y)0 9334 y FK(routine)59 b(for)g(doing)f(just)h(this.)101 b(Gi)l(v)n(en)57 b(a)h(graph)h(that)f(is)g(distrib)m(uted)h(among)f (the)g(processors)f(and)i(the)f(coordinates)g(of)g(the)g(v)n(er)m(-)0 9553 y(tices,)347 9493 y Fr(3)467 9553 y FA(P)-7 b(arMETIS)p 1235 9553 V 61 w(V3)p 1499 9553 V 60 w(P)g(ar)7 b(tGeomKw)n(a)-5 b(y)49 b FK(quickly)g(computes)e(an)h(initial)h(partitioning)g(using)f (a)g(space-\002lling)g(curv)n(e)f(method,)0 9772 y(redistrib)m(utes)53 b(the)g(graph)g(according)g(to)g(this)g(partitioning,)k(and)c(then)g (calls)f FA(P)-7 b(arMETIS)p 5371 9772 V 61 w(V3)p 5635 9772 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)53 b FK(to)h(compute)f(the)g (\002nal)0 9992 y(high-quality)38 b(partitioning.)50 b(Our)37 b(e)n(xperiments)f(ha)m(v)n(e)f(sho)l(wn)i(that)g FA(P)-7 b(arMETIS)p 4721 9992 V 61 w(V3)p 4985 9992 V 59 w(P)g(ar)7 b(tGeomKw)n(a)-5 b(y)38 b FK(is)f(often)g(tw)n(o)g(times) g(f)n(aster)p 0 10280 3120 7 v 174 10401 a Fq(2)239 10449 y FF(That)d(is,)g(we)f(\002rst)g(call)h FG(P)-5 b(arMETIS)p 1943 10449 40 7 v 46 w(V3)p 2152 10449 V 47 w(P)g(ar)5 b(tKw)n(a)l(y)33 b FF(to)h(\002nd)g(a)g(good)h(partitioning)g(of)g(a)e (graph.)44 b(Ne)n(xt)34 b(we)f(mo)n(v)n(e)i(the)f(v)n(ertices)f(of)i (the)e(graph)i(according)h(to)e(the)0 10607 y(computed)h(partitioning,) g(and)f(then)g(call)f FG(P)-5 b(arMETIS)p 2572 10607 V 47 w(V3)p 2782 10607 V 47 w(P)g(ar)5 b(tKw)n(a)l(y)32 b FF(to)i(partition)g(this)g(same,)f(b)m(ut)h(ne)m(wly)g(distrib)m (uted,)h(graph.)174 10731 y Fq(3)239 10779 y FG(P)-5 b(arMETIS)p 856 10779 V 46 w(V3)p 1065 10779 V 48 w(P)g(ar)5 b(tGeomKw)n(a)l(y)32 b FF(requires)i(the)f(coordinates)i(of)f(the)f (centers)h(of)g(each)f(element.)3858 11298 y FK(6)p eop %%Page: 7 7 7 6 bop 0 166 a FK(than)41 b FA(P)-7 b(arMETIS)p 1095 166 50 7 v 61 w(V3)p 1359 166 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)p FK(,)41 b(and)h(achie)l(v)n(es)d(identical)i(partition)i(quality) -11 b(.)203 385 y FA(P)h FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)39 b FK(also)32 b(pro)n(vides)f(the)h FA(P)-7 b(arMETIS)p 2847 385 V 61 w(P)g(ar)7 b(tGeom)34 b FK(function)f(for)f(partitioning)i(unstructured)e(graphs)g(when)g (coordinates)0 604 y(for)53 b(the)f(v)n(ertices)f(are)h(a)m(v)l (ailable.)82 b FA(P)-7 b(arMETIS)p 2807 604 V 61 w(P)g(ar)7 b(tGeom)54 b FK(computes)e(a)g(partitioning)h(based)f(only)g(on)g(the)h (space-\002lling)f(curv)n(e)0 824 y(method.)f(Therefore,)41 b(it)g(is)g(e)n(xtremely)f(f)n(ast)h(\(often)h(5)f(to)g(10)g(times)g(f) n(aster)g(than)g FA(P)-7 b(arMETIS)p 5437 824 V 60 w(P)g(ar)7 b(tGeomKw)n(a)-5 b(y)p FK(\),)42 b(b)m(ut)f(it)h(computes)0 1043 y(poor)k(quality)g(partitionings)g(\(it)g(may)g(cut)f(2)h(to)g(10) f(times)h(more)g(edges)e(than)i FA(P)-7 b(arMETIS)p 5346 1043 V 61 w(P)g(ar)7 b(tGeomKw)n(a)-5 b(y)p FK(\).)65 b(This)46 b(routine)g(can)0 1262 y(be)53 b(useful)h(for)g(certain)f (computations)h(in)g(which)f(the)g(use)g(of)h(space-\002lling)g(curv)n (es)e(is)i(the)f(appropriate)h(partitioning)g(technique)0 1481 y(\()p Fs(e)n(.g)o FK(.,)41 b Fy(n)7 b FK(-body)42 b(computations\).)0 1936 y Ft(3.2)199 b(P)-6 b(ar)t(titioning)56 b(Meshes)e(Directl)m(y)4 2255 y FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)t FK(,)69 b(V)-18 b(ersion)67 b(3.0)g(also)g(pro)n(vides)f(ne)l(w)h(routines)h(that)f (support)h(the)f(computation)g(of)h(partitionings)g(and)f(repartition-) 0 2474 y(ings)57 b(gi)l(v)n(en)g Fs(meshes)g FK(\(and)g(not)h(graphs\)) g(as)f(inputs.)99 b(In)58 b(particular)-7 b(,)62 b FA(P)-7 b(arMETIS)p 4910 2474 V 61 w(V3)p 5174 2474 V 60 w(P)g(ar)7 b(tMeshKw)n(a)-5 b(y)58 b FK(tak)n(e)g(a)f(mesh)h(as)f(input)0 2693 y(and)71 b(computes)g(a)g(partitioning)i(of)e(the)h(mesh)f (elements.)140 b(Internally)-11 b(,)79 b FA(P)-7 b(arMETIS)p 5213 2693 V 61 w(V3)p 5477 2693 V 60 w(P)g(ar)7 b(tMeshKw)n(a)-5 b(y)72 b FK(uses)f(a)g(mesh-to-)0 2912 y(graph)56 b(routine)h(and)e (then)h(calls)g(the)g(same)f(core)h(partitioning)g(routine)h(that)f(is) g(used)f(by)h(both)g FA(P)-7 b(arMETIS)p 6487 2912 V 61 w(V3)p 6751 2912 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)56 b FK(and)0 3132 y FA(P)-7 b(arMETIS)p 768 3132 V 61 w(V3)p 1032 3132 V 60 w(P)g(ar)7 b(tGeomKw)n(a)-5 b(y)p FK(.)203 3351 y FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)65 b FK(pro)n(vides)57 b(no)h(such)f(routines)h(for)h (computing)f(adapti)l(v)n(e)f(repartitionings)i(directly)f(from)h (meshes.)99 b(Ho)l(we)l(v)n(er)-7 b(,)61 b(it)0 3570 y(does)h(pro)n(vide)h(the)g(routine)g FA(P)-7 b(arMETIS)p 2502 3570 V 61 w(V3)p 2766 3570 V 60 w(Mesh2Dual)64 b 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sf 1800 2850 m gs 1 -1 sc (3) col-1 sh gr /Times-Roman ff 150.00 scf sf 1950 2850 m gs 1 -1 sc (7) col-1 sh gr /Times-Roman ff 150.00 scf sf 1050 2850 m gs 1 -1 sc (5) col-1 sh gr /Times-Roman ff 150.00 scf sf 2100 2850 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 150.00 scf sf 2250 2850 m gs 1 -1 sc (4) col-1 sh gr /Times-Roman ff 150.00 scf sf 2700 2850 m gs 1 -1 sc (9) col-1 sh gr /Times-Roman ff 150.00 scf sf 2550 2850 m gs 1 -1 sc (3) col-1 sh gr /Times-Roman ff 150.00 scf sf 2400 2850 m gs 1 -1 sc (8) col-1 sh gr /Times-Roman ff 150.00 scf sf 3375 2850 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 150.00 scf sf 3525 2850 m gs 1 -1 sc (5) col-1 sh gr /Times-Roman ff 150.00 scf sf 3675 2850 m gs 1 -1 sc (7) col-1 sh gr /Times-Roman ff 150.00 scf sf 3825 2850 m gs 1 -1 sc (11) col-1 sh gr /Times-Roman ff 150.00 scf sf 4050 2850 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 150.00 scf sf 4200 2850 m gs 1 -1 sc (6) col-1 sh gr /Times-Roman ff 150.00 scf sf 4350 2850 m gs 1 -1 sc (8) col-1 sh gr /Times-Roman ff 150.00 scf sf 4500 2850 m gs 1 -1 sc (12) col-1 sh gr /Times-Roman ff 150.00 scf sf 4725 2850 m gs 1 -1 sc (3) col-1 sh gr /Times-Roman ff 150.00 scf sf 4875 2850 m gs 1 -1 sc (7) col-1 sh gr /Times-Roman ff 150.00 scf sf 5025 2850 m gs 1 -1 sc (9) col-1 sh gr /Times-Roman ff 150.00 scf sf 5175 2850 m gs 1 -1 sc (13) col-1 sh gr /Times-Roman ff 150.00 scf sf 5400 2850 m gs 1 -1 sc (4) col-1 sh gr /Times-Roman ff 150.00 scf sf 5550 2850 m gs 1 -1 sc (8) col-1 sh gr /Times-Roman ff 150.00 scf sf 5700 2850 m gs 1 -1 sc (14) col-1 sh gr /Times-Roman ff 150.00 scf sf 2850 2850 m gs 1 -1 sc (0) col-1 sh gr /Times-Roman ff 150.00 scf sf 3000 2850 m gs 1 -1 sc (6) col-1 sh gr /Times-Roman ff 150.00 scf sf 3150 2850 m gs 1 -1 sc (10) col-1 sh gr /Times-Roman ff 150.00 scf sf 5925 2850 m gs 1 -1 sc (5) col-1 sh gr /Times-Roman ff 150.00 scf sf 6075 2850 m gs 1 -1 sc (11) col-1 sh gr /Times-Roman ff 150.00 scf sf 6300 2850 m gs 1 -1 sc (6) col-1 sh gr /Times-Roman ff 150.00 scf sf 6450 2850 m gs 1 -1 sc (10) col-1 sh gr /Times-Roman ff 150.00 scf sf 6675 2850 m gs 1 -1 sc (12) col-1 sh gr /Times-Roman ff 150.00 scf sf 6900 2850 m gs 1 -1 sc (7) col-1 sh gr /Times-Roman ff 150.00 scf sf 7050 2850 m gs 1 -1 sc (11) col-1 sh gr /Times-Roman ff 150.00 scf sf 7275 2850 m gs 1 -1 sc (13) col-1 sh gr /Times-Roman ff 150.00 scf sf 7500 2850 m gs 1 -1 sc (8) col-1 sh gr /Times-Roman ff 150.00 scf sf 7650 2850 m gs 1 -1 sc (12) col-1 sh gr /Times-Roman ff 150.00 scf sf 7875 2850 m gs 1 -1 sc (14) col-1 sh gr /Times-Roman ff 150.00 scf sf 8100 2850 m gs 1 -1 sc (9) col-1 sh gr /Times-Roman ff 150.00 scf sf 8250 2850 m gs 1 -1 sc (13) col-1 sh gr % Polyline n 150 2250 m 8550 2250 l 8550 3000 l 150 3000 l cp gs col-1 s gr /Times-Roman ff 150.00 scf sf 600 2550 m gs 1 -1 sc (xadj) dup sw pop neg 0 rm col-1 sh gr /Times-Roman ff 150.00 scf sf 600 2850 m gs 1 -1 sc (adjncy) dup sw pop neg 0 rm col-1 sh gr /Times-Roman ff 180.00 scf sf 150 2175 m gs 1 -1 sc (Description of the graph on a serial computer \(serial MeTiS\)) col-1 sh gr % Polyline n 3300 600 m 4500 600 l gs col-1 s gr % Polyline n 3600 300 m 3600 900 l gs col-1 s gr % Polyline n 3300 300 m 4500 300 l 4500 900 l 3300 900 l 3300 300 l cp gs col-1 s gr % Polyline n 3900 300 m 3900 900 l gs col-1 s gr % Polyline n 4200 300 m 4200 900 l gs col-1 s gr /Times-Roman ff 150.00 scf sf 3150 450 m gs 1 -1 sc (0) col-1 sh gr /Times-Roman ff 150.00 scf sf 3450 450 m gs 1 -1 sc (1) col-1 sh gr /Times-Roman ff 150.00 scf sf 3750 450 m gs 1 -1 sc (2) col-1 sh gr /Times-Roman ff 150.00 scf sf 4050 450 m gs 1 -1 sc (3) col-1 sh gr /Times-Roman ff 150.00 scf sf 4350 450 m gs 1 -1 sc (4) col-1 sh gr /Times-Roman ff 150.00 scf sf 3150 750 m gs 1 -1 sc (5) col-1 sh gr /Times-Roman ff 150.00 scf sf 3450 750 m gs 1 -1 sc (6) col-1 sh gr /Times-Roman ff 150.00 scf sf 3750 750 m gs 1 -1 sc (7) col-1 sh gr /Times-Roman ff 150.00 scf sf 4050 750 m gs 1 -1 sc (8) col-1 sh gr /Times-Roman ff 150.00 scf sf 4350 750 m gs 1 -1 sc (9) col-1 sh gr /Times-Roman ff 150.00 scf sf 4425 1125 m gs 1 -1 sc (14) col-1 sh gr /Times-Roman ff 150.00 scf sf 4125 1125 m gs 1 -1 sc (13) col-1 sh gr /Times-Roman ff 150.00 scf sf 3825 1125 m gs 1 -1 sc (12) col-1 sh gr /Times-Roman ff 150.00 scf sf 3525 1125 m gs 1 -1 sc (11) col-1 sh gr /Times-Roman ff 150.00 scf sf 3225 1125 m gs 1 -1 sc (10) col-1 sh gr /Helvetica-Bold ff 210.00 scf sf 3900 1500 m gs 1 -1 sc (\(a\) A sample graph) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold ff 210.00 scf sf 3900 3375 m gs 1 -1 sc (\(b\) Serial CSR format) dup sw pop 2 div neg 0 rm col-1 sh gr /Helvetica-Bold ff 210.00 scf sf 3900 7950 m gs 1 -1 sc (\(c\) Distributed CSR format) dup sw pop 2 div neg 0 rm col-1 sh gr $F2psEnd rs %%EndDocument @endspecial 0 5844 a Fx(Figure)49 b(5)p FK(:)74 b Fw(An)48 b(e)l(xample)g(of)g(the)g(par)o(ameters)g(passed)f(to)52 b(P)-6 b Fv(A)8 b(R)g Fw(M)-9 b Fv(E)-34 b Fw(T)g Fv(I)p Fw(S)55 b(in)48 b(a)g(three)g(processor)g(case)n(.)78 b(The)48 b(arr)o(a)l(ys)h Fj(vwgt)e Fw(and)g Fj(adjwgt)f Fw(are)0 6043 y(assumed)37 b(to)h(be)f(NULL.)0 6377 y FK(processor)f(needs)f(its)h(local)h Fj(xadj)d FK(array)j(to)f(point)h (to)g(where)f(each)f(of)i(its)f(local)g(v)n(ertices')g(adjacenc)n(y)f (lists)h(be)n(gin)f(and)i(end.)49 b(Thus,)37 b(if)0 6597 y(we)i(tak)n(e)h(all)f(the)h(local)f Fj(adjncy)e FK(arrays)j(and)f (concatenate)f(them,)i(we)f(will)h(get)f(e)n(xactly)g(the)g(same)g Fj(adjncy)e FK(array)j(that)g(is)f(used)g(in)0 6816 y(the)k(serial)g (CSR.)g(Ho)l(we)l(v)n(er)-7 b(,)42 b(concatenating)g(the)i(local)f Fj(xadj)e FK(arrays)i(will)h(not)f(gi)l(v)n(e)g(us)g(the)g(serial)g Fj(xadj)f FK(array)-11 b(.)56 b(This)43 b(is)g(because)0 7035 y(the)50 b(entries)f(in)h(each)f(local)h Fj(xadj)e FK(must)i(point)g(to)g(their)h(local)e Fj(adjncy)f FK(array)-11 b(,)52 b(and)d(so,)i Fj(xadj[)p FK(0)p Fj(])d FK(is)i(zero)f(for)i(all) f(processors.)0 7254 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7148 y FD(tpwgts)277 b FK(An)52 b(array)g(of)g(size)f Fj(ncon)g FK(x)h Fj(nparts)d FK(that)j(is)g(used)f(to)h(specify)f(the)h(fraction)g(of)h(v)n(erte)n (x)d(weight)i(that)g(should)1162 7367 y(be)44 b(distrib)m(uted)g(to)g (each)f(sub-domain)h(for)h(each)e(balance)g(constraint.)58 b(If)45 b(all)f(of)g(the)g(sub-domains)f(are)h(to)g(be)g(of)1162 7587 y(the)e(same)e(size)h(for)h(e)l(v)n(ery)f(v)n(erte)n(x)f(weight,)h (then)h(each)e(of)i(the)g Fj(ncon)e FK(x)h Fj(nparts)e FK(elements)i(should)g(be)h(set)f(to)g(a)1162 7806 y(v)l(alue)c(of)g (1/)p Fj(nparts)p FK(.)47 b(If)38 b Fj(ncon)d FK(is)i(greater)f(than)h (one,)g(the)g(tar)m(get)g(sub-domain)g(weights)f(for)i(each)e (sub-domain)1162 8025 y(are)50 b(stored)g(contiguously)f(\(similar)i (to)f(the)g Fj(vwgt)e FK(array\).)76 b(Note)50 b(that)g(the)g(sum)f(of) h(all)g(of)g(the)g Fj(tpwgts)e FK(for)i(a)1162 8244 y(gi)l(v)n(e)41 b(v)n(erte)n(x)g(weight)g(should)g(be)h(one.)415 8512 y FD(ub)n(v)n(ec)336 b FK(An)42 b(array)g(of)g(size)f 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(obtained)f(by)h(setting)f(this)g(to)h(1.)60 b(Additional)45 b(options)f(for)2066 10362 y(this)i(parameter)f(can)f(be)h(obtained)g (by)h(looking)f(at)g(the)g(the)g(\002le)h Fj(defs.h)d FK(in)i(the)g Fj(ParMETIS-)2066 10581 y(Lib)39 b FK(directory)-11 b(.)51 b(The)40 b(numerical)g(v)l(alues)f(there)h(should)f(be)h(added)f (to)h(obtain)g(the)g(correct)g(v)l(alue.)2066 10800 y(The)i(def)n(ault) g(v)l(alue)f(is)g(0.)3817 11298 y(17)p eop %%Page: 18 18 18 17 bop 1162 166 a FK(options[2])222 b(This)42 b(is)f(the)h(random)g (number)f(seed)g(for)h(the)f(routine.)52 b(The)42 b(def)n(ault)f(v)l (alue)h(is)f(15.)415 452 y FD(edgecut)203 b FK(Upon)51 b(successful)f(completion,)k(the)d(number)g(of)h(edges)e(that)h(are)g (cut)g(by)h(the)f(partitioning)h(is)f(written)h(to)f(this)1162 671 y(parameter)-9 b(.)415 956 y FD(part)443 b FK(This)33 b(is)f(an)f(array)i(of)f(size)f(equal)h(to)g(the)g(number)h(of)f (locally-stored)g(v)n(ertices.)47 b(Upon)32 b(successful)f(completion)h (the)1162 1176 y(partition)43 b(v)n(ector)d(of)i(the)g(locally-stored)f (v)n(ertices)g(is)g(written)h(to)g(this)f(array)-11 b(.)51 b(\(See)42 b(discussion)e(in)i(Section)g(4.4\).)415 1461 y FD(comm)314 b FK(This)45 b(is)e(a)h(pointer)g(to)g(the)g(MPI)g (communicator)h(of)f(the)g(processes)e(that)i(call)k FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)t FK(.)46 b(F)n(or)e(most)g(programs)1162 1680 y(this)e(will)g (point)g(to)f Fj(MPI)p 2607 1680 50 7 v 59 w(COMM)p 3066 1680 V 58 w(WORLD)p FK(.)3817 11298 y(18)p eop %%Page: 19 19 19 18 bop 0 166 a FB(P)-5 b(arMETIS)p 780 166 50 7 v 60 w(V3)p 1043 166 V 60 w(P)g(ar)s(tGeomKwa)m(y)42 b FK(\(idxtype)g(*vtxdist,)g(idxtype)f(*xadj,)g(idxtype)h(*adjnc)n(y)-11 b(,)40 b(idxtype)i(*vwgt,)f(idxtype)h(*adjwgt,)2356 385 y(int)g(*wgt\003ag,)f(int)h(*num\003ag,)g(int)g(*ndims,)f(\003oat)g (*xyz,)g(int)h(*ncon,)f(int)h(*nparts,)2356 604 y(\003oat)g(*tpwgts,)f (\003oat)h(*ub)n(v)n(ec,)d(int)j(*options,)f(int)h(*edgecut,)f(idxtype) g(*part,)2356 824 y(MPI)p 2661 824 V 60 w(Comm)h(*comm\))0 1342 y FB(Description)415 1561 y FK(This)47 b(routine)g(is)g(used)f(to) h(compute)f(a)h Fy(k)10 b FK(-w)n(ay)46 b(partitioning)i(of)f(a)f (graph)h(on)66 b Fy(p)52 b FK(processors)45 b(by)i(combining)g(the)g (coordinate-)415 1780 y(based)41 b(and)g(multi-constraint)h Fy(k)10 b FK(-w)n(ay)42 b(partitioning)g(schemes.)0 2132 y FB(P)-5 b(arameter)n(s)415 2371 y FD(vtxdist)268 b FK(This)39 b(array)g(describes)f(ho)l(w)g(the)h(v)n(ertices)f(of)h(the) f(graph)h(are)g(distrib)m(uted)f(among)h(the)g(processors.)49 b(\(See)39 b(discus-)1162 2590 y(sion)j(in)f(Section)h(4.1\).)51 b(Its)41 b(contents)g(are)g(identical)h(for)g(e)l(v)n(ery)f(processor) -9 b(.)415 2824 y FD(xadj,)42 b(adjncy)1162 3043 y FK(These)52 b(store)g(the)h(\(local\))f(adjacenc)n(y)f(structure)h(of)h(the)f (graph)g(at)h(each)e(processor)-9 b(.)83 b(\(See)52 b(discussion)f(in)i (Sec-)1162 3262 y(tion)42 b(4.1\).)415 3489 y FD(vwgt,)f(adjwgt)1162 3708 y FK(These)g(store)h(the)f(weights)g(of)h(the)f(v)n(ertices)g(and) g(edges.)50 b(\(See)42 b(discussion)e(in)i(Section)f(4.1\).)415 3994 y FD(wgt\003ag)231 b FK(This)42 b(is)f(used)g(to)h(indicate)f(if)h (the)f(graph)h(is)f(weighted.)51 b Fs(wgt\003a)n(g)42 b FK(can)f(tak)n(e)g(one)h(of)f(four)i(v)l(alues:)1162 4279 y(0)166 b(No)42 b(weights)f(\(vwgt)h(and)f(adjwgt)h(are)f(both)g (NULL\).)1162 4532 y(1)166 b(W)-13 b(eights)41 b(on)h(the)f(edges)g (only)g(\(vwgt)h(is)f(NULL\).)1162 4784 y(2)166 b(W)-13 b(eights)41 b(on)h(the)f(v)n(ertices)f(only)i(\(adjwgt)g(is)f(NULL\).) 1162 5036 y(3)166 b(W)-13 b(eights)41 b(on)h(both)f(the)h(v)n(ertices)e (and)h(edges.)415 5322 y FD(num\003ag)167 b FK(This)58 b(is)f(used)g(to)h(indicate)f(the)g(numbering)h(scheme)e(that)i(is)f (used)g(for)h(the)f Fs(vtxdist)p FK(,)k Fs(xadj)p FK(,)f Fs(adjncy)p FK(,)h(and)c Fs(part)1162 5541 y FK(arrays.)51 b Fs(num\003a)n(g)42 b FK(can)f(tak)n(e)g(one)h(of)f(tw)n(o)h(v)l (alues:)1162 5827 y(0)166 b(C-style)42 b(numbering)g(that)f(starts)g (from)h(0.)1162 6079 y(1)166 b(F)n(ortran-style)42 b(numbering)g(that)g (starts)f(from)h(1.)415 6365 y FD(ndims)314 b FK(The)42 b(number)g(of)g(dimensions)f(of)g(the)h(space)e(in)i(which)f(the)h (graph)f(is)g(embedded.)415 6650 y FD(xyz)507 b FK(The)42 b(array)g(storing)f(the)h(coordinates)f(of)h(the)f(v)n(ertices)f (\(described)h(in)h(Section)g(4.2\).)415 6936 y FD(ncon)406 b FK(This)47 b(is)e(used)h(to)g(specify)f(the)h(number)g(of)h(weights)e (that)h(each)f(v)n(erte)n(x)g(has.)64 b(It)46 b(is)g(also)g(the)f (number)i(of)f(balance)1162 7155 y(constraints)41 b(that)h(must)f(be)h (satis\002ed.)415 7441 y FD(nparts)286 b FK(This)54 b(is)f(used)g(to)h (specify)f(the)g(number)h(of)f(sub-domains)g(that)h(are)f(desired.)87 b(Note)53 b(that)g(the)h(number)f(of)h(sub-)1162 7660 y(domains)42 b(is)f(independent)g(of)h(the)f(number)h(of)g(processors)e (that)i(call)f(this)g(routine.)415 7946 y FD(tpwgts)277 b FK(An)52 b(array)g(of)g(size)f Fj(ncon)g FK(x)h Fj(nparts)d FK(that)j(is)g(used)f(to)h(specify)f(the)h(fraction)g(of)h(v)n(erte)n (x)d(weight)i(that)g(should)1162 8165 y(be)44 b(distrib)m(uted)g(to)g (each)f(sub-domain)h(for)h(each)e(balance)g(constraint.)58 b(If)45 b(all)f(of)g(the)g(sub-domains)f(are)h(to)g(be)g(of)1162 8384 y(the)e(same)e(size)h(for)h(e)l(v)n(ery)f(v)n(erte)n(x)f(weight,)h (then)h(each)e(of)i(the)g Fj(ncon)e FK(x)h Fj(nparts)e FK(elements)i(should)g(be)h(set)f(to)g(a)1162 8603 y(v)l(alue)c(of)g (1/)p Fj(nparts)p FK(.)47 b(If)38 b Fj(ncon)d FK(is)i(greater)f(than)h (one,)g(the)g(tar)m(get)g(sub-domain)g(weights)f(for)i(each)e (sub-domain)1162 8822 y(are)50 b(stored)g(contiguously)f(\(similar)i (to)f(the)g Fj(vwgt)e FK(array\).)76 b(Note)50 b(that)g(the)g(sum)f(of) h(all)g(of)g(the)g Fj(tpwgts)e FK(for)i(a)1162 9041 y(gi)l(v)n(e)41 b(v)n(erte)n(x)g(weight)g(should)g(be)h(one.)415 9327 y FD(ub)n(v)n(ec)336 b FK(An)42 b(array)g(of)g(size)f Fj(ncon)f FK(that)i(is)g(used)f(to)h(specify)f(the)h(imbalance)f (tolerance)g(for)i(each)e(v)n(erte)n(x)g(weight,)g(with)h(1)1162 9546 y(being)47 b(perfect)g(balance)e(and)i Fj(nparts)d FK(being)j(perfect)g(imbalance.)66 b(A)46 b(v)l(alue)g(of)h(1.05)g(for) g(each)f(of)h(the)f Fj(ncon)1162 9765 y FK(weights)41 b(is)h(recommended.)415 10051 y FD(options)231 b FK(This)36 b(is)f(an)g(array)g(of)h(inte)n(gers)f(that)g(is)g(used)g(to)g(pass)g (parameters)f(to)i(the)f(routine.)49 b(Their)36 b(meanings)f(are)g (identical)1162 10270 y(to)42 b(those)f(of)h FA(P)-7 b(arMETIS)p 2673 10270 V 61 w(V3)p 2937 10270 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)p FK(.)415 10556 y FD(edgecut)203 b FK(Upon)51 b(successful)f(completion,)k(the)d(number)g(of)h(edges)e (that)h(are)g(cut)g(by)h(the)f(partitioning)h(is)f(written)h(to)f(this) 1162 10775 y(parameter)-9 b(.)3817 11298 y(19)p eop %%Page: 20 20 20 19 bop 415 166 a FD(part)443 b FK(This)33 b(is)f(an)f(array)i(of)f (size)f(equal)h(to)g(the)g(number)h(of)f(locally-stored)g(v)n(ertices.) 47 b(Upon)32 b(successful)f(completion)h(the)1162 385 y(partition)43 b(v)n(ector)d(of)i(the)g(locally-stored)f(v)n(ertices)g (is)g(written)h(to)g(this)f(array)-11 b(.)51 b(\(See)42 b(discussion)e(in)i(Section)g(4.4\).)415 671 y FD(comm)314 b FK(This)45 b(is)e(a)h(pointer)g(to)g(the)g(MPI)g(communicator)h(of)f (the)g(processes)e(that)i(call)k FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)t FK(.)46 b(F)n(or)e(most)g (programs)1162 890 y(this)e(will)g(point)g(to)f Fj(MPI)p 2607 890 50 7 v 59 w(COMM)p 3066 890 V 58 w(WORLD)p FK(.)0 1242 y FB(Note)415 1461 y FK(The)58 b(quality)g(of)g(the)g (partitionings)g(computed)g(by)g FA(P)-7 b(arMETIS)p 4309 1461 V 61 w(V3)p 4573 1461 V 59 w(P)g(ar)7 b(tGeomKw)n(a)-5 b(y)59 b FK(are)f(comparable)f(to)h(those)f(pro-)415 1680 y(duced)41 b(by)h FA(P)-7 b(arMETIS)p 1829 1680 V 61 w(V3)p 2093 1680 V 59 w(P)g(ar)7 b(tKw)n(a)-5 b(y)p FK(.)51 b(Ho)l(we)l(v)n(er)-7 b(,)41 b(the)g(run)h(time)g(of)f(the)h (routine)g(may)f(be)g(up)h(to)g(twice)f(as)g(f)n(ast.)3817 11298 y(20)p eop %%Page: 21 21 21 20 bop 0 166 a FB(P)-5 b(arMETIS)p 780 166 50 7 v 60 w(V3)p 1043 166 V 60 w(P)g(ar)s(tGeom)42 b FK(\(idxtype)g(*vtxdist,) f(int)h(*ndims,)f(\003oat)h(*xyz,)f(idxtype)g(*part,)g(MPI)p 5939 166 V 60 w(Comm)h(*comm\))0 684 y FB(Description)415 903 y FK(This)64 b(routine)g(is)g(used)f(to)h(compute)g(a)82 b Fy(p)5 b FK(-w)n(ay)65 b(partitioning)f(of)h(a)e(graph)h(on)83 b Fy(p)69 b FK(processors)63 b(using)g(a)h(coordinate-based)415 1122 y(space-\002lling)42 b(curv)n(es)e(method.)0 1474 y FB(P)-5 b(arameter)n(s)415 1714 y FD(vtxdist)268 b FK(This)39 b(array)g(describes)f(ho)l(w)g(the)h(v)n(ertices)f(of)h(the) f(graph)h(are)g(distrib)m(uted)f(among)h(the)g(processors.)49 b(\(See)39 b(discus-)1162 1933 y(sion)j(in)f(Section)h(4.1\).)51 b(Its)41 b(contents)g(are)g(identical)h(for)g(e)l(v)n(ery)f(processor) -9 b(.)415 2218 y FD(ndims)314 b FK(The)42 b(number)g(of)g(dimensions)f (of)g(the)h(space)e(in)i(which)f(the)h(graph)f(is)g(embedded.)415 2504 y FD(xyz)507 b FK(The)42 b(array)g(storing)f(the)h(coordinates)f (of)h(the)f(v)n(ertices)f(\(described)h(in)h(Section)g(4.2\).)415 2790 y FD(part)443 b FK(This)48 b(is)g(an)g(array)g(of)g(size)f(equal)g (to)h(the)g(number)g(of)g(locally)g(stored)g(v)n(ertices.)69 b(Upon)48 b(successful)e(completion)1162 3009 y(stores)41 b(the)h(partition)g(v)n(ector)f(of)h(the)f(locally)h(stored)f(graph)g (\(described)g(in)h(Section)g(4.4\).)415 3294 y FD(comm)314 b FK(This)45 b(is)e(a)h(pointer)g(to)g(the)g(MPI)g(communicator)h(of)f (the)g(processes)e(that)i(call)k FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)t FK(.)46 b(F)n(or)e(most)g (programs)1162 3514 y(this)e(will)g(point)g(to)f Fj(MPI)p 2607 3514 V 59 w(COMM)p 3066 3514 V 58 w(WORLD)p FK(.)0 3866 y FB(Note)415 4085 y FK(The)64 b(quality)h(of)f(the)h (partitionings)f(computed)g(by)h FA(P)-7 b(arMETIS)p 4354 4085 V 60 w(V3)p 4617 4085 V 60 w(P)g(ar)7 b(tGeom)66 b FK(are)e(signi\002cantly)g(w)n(orse)g(than)g(those)415 4304 y(produced)41 b(by)h FA(P)-7 b(arMETIS)p 2050 4304 V 61 w(V3)p 2314 4304 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)41 b FK(and)h FA(P)-7 b(arMETIS)p 4158 4304 V 61 w(V3)p 4422 4304 V 59 w(P)g(ar)7 b(tGeomKw)n(a)-5 b(y)p FK(.)3817 11298 y(21)p eop %%Page: 22 22 22 21 bop 0 166 a FB(P)-5 b(arMETIS)p 780 166 50 7 v 60 w(V3)p 1043 166 V 60 w(P)g(ar)s(tMeshKwa)m(y)43 b FK(\(idxtype)f(*elmdist,)f(idxtype)h(*eptr)-7 b(,)42 b(idxtype)f(*eind,)g(idxtype)h(*elmwgt,)2310 385 y(int)g(*wgt\003ag,)f (int)h(*num\003ag,)g(int)f(*ncon,)g(int)h(*ncommonnodes,)f(int)g (*nparts,)2310 604 y(\003oat)h(*tpwgts,)f(\003oat)h(*ub)n(v)n(ec,)d (int)j(*options,)f(int)h(*edgecut,)e(idxtype)i(*part,)2310 824 y(MPI)p 2615 824 V 60 w(Comm)g(*comm\))0 1342 y FB(Description)415 1561 y FK(This)d(routine)h(is)f(used)f(to)h(compute)g(a)g Fy(k)10 b FK(-w)n(ay)39 b(partitioning)h(of)f(a)g Fs(mesh)f FK(on)58 b Fy(p)45 b FK(processors.)k(The)39 b(mesh)f(can)h(contain)g (elements)415 1780 y(of)j(dif)l(ferent)g(types.)0 2132 y FB(P)-5 b(arameter)n(s)415 2371 y FD(elmdist)231 b FK(This)47 b(array)g(describes)e(ho)l(w)i(the)f(elements)g(of)h(the)f (mesh)h(are)f(distrib)m(uted)g(among)h(the)g(processors.)65 b(It)47 b(is)f(anal-)1162 2590 y(ogous)64 b(to)g(the)g Fj(vtxdist)d FK(array)-11 b(.)119 b(Its)64 b(contents)f(are)h (identical)g(for)g(e)l(v)n(ery)f(processor)-9 b(.)118 b(\(See)64 b(discussion)f(in)1162 2809 y(Section)42 b(4.3\).)415 3036 y FD(eptr)-15 b(,)41 b(eind)1162 3256 y FK(These)64 b(arrays)g(speci\002es)f(the)g(elements)h(that)g(are)g(stored)g (locally)g(at)g(each)f(processor)-9 b(.)118 b(\(See)64 b(discussion)f(in)1162 3475 y(Section)42 b(4.3\).)415 3760 y FD(elmwgt)231 b FK(This)42 b(array)g(stores)e(the)i(weights)f (of)h(the)f(elements.)50 b(\(See)42 b(discussion)e(in)i(Section)g (4.3\).)415 4046 y FD(wgt\003ag)231 b FK(This)42 b(is)f(used)g(to)h (indicate)f(if)h(the)f(graph)h(is)f(weighted.)51 b Fs(wgt\003a)n(g)42 b FK(can)f(tak)n(e)g(one)h(of)f(four)i(v)l(alues:)1162 4332 y(0)166 b(No)42 b(weights)f(\(vwgt)h(and)f(adjwgt)h(are)f(both)g (NULL\).)1162 4584 y(1)166 b(W)-13 b(eights)41 b(on)h(the)f(edges)g (only)g(\(vwgt)h(is)f(NULL\).)1162 4836 y(2)166 b(W)-13 b(eights)41 b(on)h(the)f(v)n(ertices)f(only)i(\(adjwgt)g(is)f(NULL\).) 1162 5089 y(3)166 b(W)-13 b(eights)41 b(on)h(both)f(the)h(v)n(ertices)e (and)h(edges.)415 5374 y FD(num\003ag)167 b FK(This)41 b(is)f(used)f(to)i(indicate)f(the)g(numbering)g(scheme)g(that)g(is)g (used)f(for)i(the)f Fs(elmdist)p FK(,)g Fs(elements)p FK(,)f(and)h Fs(part)g FK(arrays.)1162 5593 y Fs(num\003a)n(g)i FK(can)f(tak)n(e)h(one)f(of)h(tw)n(o)g(v)l(alues:)1162 5879 y(0)166 b(C-style)42 b(numbering)g(that)f(starts)g(from)h(0.)1162 6131 y(1)166 b(F)n(ortran-style)42 b(numbering)g(that)g(starts)f(from)h (1.)415 6417 y FD(ncon)406 b FK(This)47 b(is)e(used)h(to)g(specify)f (the)h(number)g(of)h(weights)e(that)h(each)f(v)n(erte)n(x)g(has.)64 b(It)46 b(is)g(also)g(the)f(number)i(of)f(balance)1162 6636 y(constraints)41 b(that)h(must)f(be)h(satis\002ed.)415 6833 y FD(ncommonnodes)1162 7052 y FK(This)i(parameter)g(determines)g (the)f(de)n(gree)g(of)i(connecti)l(vity)e(among)h(the)g(v)n(ertices)f (in)h(the)f(dual)h(graph.)58 b(Speci\002-)1162 7271 y(cally)-11 b(,)43 b(an)f(edge)g(is)h(placed)f(between)g(an)n(y)f(tw)n(o)j (elements)d(if)j(and)e(only)h(if)g(the)n(y)f(share)g(at)g(least)g(this) h(man)n(y)f(nodes.)1162 7490 y(This)53 b(v)l(alue)e(should)h(be)g (greater)g(than)g(zero,)i(and)e(for)h(most)f(meshes)f(a)h(v)l(alue)f (of)i(tw)n(o)f(will)h(create)e(reasonable)1162 7710 y(dual)45 b(graphs.)61 b(Ho)l(we)l(v)n(er)-7 b(,)44 b(depending)g(on)h(the)g (type)g(of)g(elements)f(in)h(the)g(mesh,)f(v)l(alues)g(greater)h(than)g (tw)n(o)g(may)1162 7929 y(also)50 b(be)g(v)l(alid)g(choices.)77 b(F)n(or)50 b(e)n(xample,)h(for)g(meshes)f(containing)g(only)h (triangular)-7 b(,)53 b(tetrahedral,)f(he)n(xahedral,)1162 8148 y(or)42 b(rectangular)g(elements,)e(this)h(parameter)h(can)f(be)g (set)g(to)g(tw)n(o,)h(three,)f(four)-7 b(,)42 b(or)g(tw)n(o,)f (respecti)l(v)n(ely)-11 b(.)1162 8400 y(Note)51 b(that)f(setting)h (this)f(parameter)g(to)h(a)f(small)h(v)l(alue)f(will)h(increase)e(the)h (number)h(of)g(edges)f(in)g(the)h(resulting)1162 8620 y(dual)42 b(graph)f(and)h(the)f(corresponding)g(partitioning)i(time.) 415 8905 y FD(nparts)286 b FK(This)54 b(is)f(used)g(to)h(specify)f(the) g(number)h(of)f(sub-domains)g(that)h(are)f(desired.)87 b(Note)53 b(that)g(the)h(number)f(of)h(sub-)1162 9124 y(domains)42 b(is)f(independent)g(of)h(the)f(number)h(of)g(processors)e (that)i(call)f(this)g(routine.)415 9410 y FD(tpwgts)277 b FK(An)52 b(array)g(of)g(size)f Fj(ncon)g FK(x)h Fj(nparts)d FK(that)j(is)g(used)f(to)h(specify)f(the)h(fraction)g(of)h(v)n(erte)n (x)d(weight)i(that)g(should)1162 9629 y(be)44 b(distrib)m(uted)g(to)g (each)f(sub-domain)h(for)h(each)e(balance)g(constraint.)58 b(If)45 b(all)f(of)g(the)g(sub-domains)f(are)h(to)g(be)g(of)1162 9848 y(the)e(same)e(size)h(for)h(e)l(v)n(ery)f(v)n(erte)n(x)f(weight,)h (then)h(each)e(of)i(the)g Fj(ncon)e FK(x)h Fj(nparts)e FK(elements)i(should)g(be)h(set)f(to)g(a)1162 10067 y(v)l(alue)c(of)g (1/)p Fj(nparts)p FK(.)47 b(If)38 b Fj(ncon)d FK(is)i(greater)f(than)h (one,)g(the)g(tar)m(get)g(sub-domain)g(weights)f(for)i(each)e (sub-domain)1162 10287 y(are)50 b(stored)g(contiguously)f(\(similar)i (to)f(the)g Fj(vwgt)e FK(array\).)76 b(Note)50 b(that)g(the)g(sum)f(of) h(all)g(of)g(the)g Fj(tpwgts)e FK(for)i(a)1162 10506 y(gi)l(v)n(e)41 b(v)n(erte)n(x)g(weight)g(should)g(be)h(one.)3817 11298 y(22)p eop %%Page: 23 23 23 22 bop 415 166 a FD(ub)n(v)n(ec)336 b FK(An)42 b(array)g(of)g(size)f Fj(ncon)f FK(that)i(is)g(used)f(to)h(specify)f(the)h(imbalance)f (tolerance)g(for)i(each)e(v)n(erte)n(x)g(weight,)g(with)h(1)1162 385 y(being)47 b(perfect)g(balance)e(and)i Fj(nparts)d FK(being)j(perfect)g(imbalance.)66 b(A)46 b(v)l(alue)g(of)h(1.05)g(for) g(each)f(of)h(the)f Fj(ncon)1162 604 y FK(weights)41 b(is)h(recommended.)415 890 y FD(options)231 b FK(This)36 b(is)f(an)g(array)g(of)h(inte)n(gers)f(that)g(is)g(used)g(to)g(pass)g (parameters)f(to)i(the)f(routine.)49 b(Their)36 b(meanings)f(are)g (identical)1162 1109 y(to)42 b(those)f(of)h FA(P)-7 b(arMETIS)p 2673 1109 50 7 v 61 w(V3)p 2937 1109 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)p FK(.)415 1395 y FD(edgecut)203 b FK(Upon)51 b(successful)f(completion,)k(the)d(number)g(of)h(edges)e(that)h(are)g (cut)g(by)h(the)f(partitioning)h(is)f(written)h(to)f(this)1162 1614 y(parameter)-9 b(.)415 1900 y FD(part)443 b FK(This)33 b(is)f(an)f(array)i(of)f(size)f(equal)h(to)g(the)g(number)h(of)f (locally-stored)g(v)n(ertices.)47 b(Upon)32 b(successful)f(completion)h (the)1162 2119 y(partition)43 b(v)n(ector)d(of)i(the)g(locally-stored)f (v)n(ertices)g(is)g(written)h(to)g(this)f(array)-11 b(.)51 b(\(See)42 b(discussion)e(in)i(Section)g(4.4\).)415 2404 y FD(comm)314 b FK(This)45 b(is)e(a)h(pointer)g(to)g(the)g(MPI)g (communicator)h(of)f(the)g(processes)e(that)i(call)k FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)t FK(.)46 b(F)n(or)e(most)g(programs)1162 2624 y(this)e(will)g (point)g(to)f Fj(MPI)p 2607 2624 V 59 w(COMM)p 3066 2624 V 58 w(WORLD)p FK(.)3817 11298 y(23)p eop %%Page: 24 24 24 23 bop 0 166 a Ft(5.2)199 b(Graph)54 b(Repar)t(titioning)0 476 y FB(P)-5 b(arMETIS)p 780 476 50 7 v 60 w(V3)p 1043 476 V 60 w(AdaptiveRepar)s(t)45 b FK(\(idxtype)d(*vtxdist,)f(idxtype)g (*xadj,)g(idxtype)h(*adjnc)n(y)-11 b(,)40 b(idxtype)i(*vwgt,)f(idxtype) h(*vsize,)2365 695 y(idxtype)f(*adjwgt,)g(int)h(*wgt\003ag,)f(int)h (*num\003ag,)f(int)h(*ncon,)f(int)h(*nparts,)f(\003oat)h(*tpwgts,)2365 914 y(\003oat)f(*ub)n(v)n(ec,)f(\003oat)i(*itr)-7 b(,)42 b(int)g(*options,)f(int)g(*edgecut,)g(idxtype)g(*part,)2365 1133 y(MPI)p 2670 1133 V 60 w(Comm)g(*comm\))0 1570 y FB(Description)415 1789 y FK(This)h(routine)g(is)f(used)g(to)h(balance) e(the)i(w)n(ork)g(load)f(of)h(a)f(graph)h(that)f(corresponds)g(to)h(an) f(adapti)l(v)n(ely)g(re\002ned)g(mesh.)0 2123 y FB(P)-5 b(arameter)n(s)415 2344 y FD(vtxdist)268 b FK(This)39 b(array)g(describes)f(ho)l(w)g(the)h(v)n(ertices)f(of)h(the)f(graph)h (are)g(distrib)m(uted)f(among)h(the)g(processors.)49 b(\(See)39 b(discus-)1162 2563 y(sion)j(in)f(Section)h(4.1\).)51 b(Its)41 b(contents)g(are)g(identical)h(for)g(e)l(v)n(ery)f(processor) -9 b(.)415 2778 y FD(xadj,)42 b(adjncy)1162 2998 y FK(These)52 b(store)g(the)h(\(local\))f(adjacenc)n(y)f(structure)h(of)h(the)f (graph)g(at)h(each)e(processor)-9 b(.)83 b(\(See)52 b(discussion)f(in)i (Sec-)1162 3217 y(tion)42 b(4.1\).)415 3426 y FD(vwgt,)f(adjwgt)1162 3645 y FK(These)g(store)h(the)f(weights)g(of)h(the)f(v)n(ertices)g(and) g(edges.)50 b(\(See)42 b(discussion)e(in)i(Section)f(4.1\).)415 3912 y FD(vsize)405 b FK(This)46 b(array)f(stores)g(the)g(size)f(of)i (the)f(v)n(ertices)f(with)i(respect)e(to)i(redistrib)m(ution)g(costs.) 61 b(Hence,)45 b(v)n(ertices)f(associ-)1162 4131 y(ated)j(with)g(mesh)g (elements)f(that)h(require)h(a)e(lot)i(of)f(memory)h(will)f(ha)m(v)n(e) f(lar)m(ger)h(corresponding)g(entries)g(in)g(this)1162 4351 y(array)-11 b(.)52 b(Otherwise,)40 b(this)h(array)h(is)f(similar)h (to)g(the)f Fj(vwgt)f FK(array)-11 b(.)51 b(\(See)42 b(discussion)e(in)i(Section)g(4.1\).)415 4618 y FD(wgt\003ag)231 b FK(This)42 b(is)f(used)g(to)h(indicate)f(if)h(the)f(graph)h(is)f (weighted.)51 b Fs(wgt\003a)n(g)42 b FK(can)f(tak)n(e)g(one)h(of)f (four)i(v)l(alues:)1162 4886 y(0)166 b(No)42 b(weights)f(\(vwgt)h(and)f (adjwgt)h(are)f(both)g(NULL\).)1162 5129 y(1)166 b(W)-13 b(eights)41 b(on)h(the)f(edges)g(only)g(\(vwgt)h(is)f(NULL\).)1162 5372 y(2)166 b(W)-13 b(eights)41 b(on)h(the)f(v)n(ertices)f(only)i (\(adjwgt)g(is)f(NULL\).)1162 5616 y(3)166 b(W)-13 b(eights)41 b(on)h(both)f(the)h(v)n(ertices)e(and)h(edges.)415 5883 y FD(num\003ag)167 b FK(This)58 b(is)f(used)g(to)h(indicate)f(the)g (numbering)h(scheme)e(that)i(is)f(used)g(for)h(the)f Fs(vtxdist)p FK(,)k Fs(xadj)p FK(,)f Fs(adjncy)p FK(,)h(and)c Fs(part)1162 6102 y FK(arrays.)51 b Fs(num\003a)n(g)42 b FK(can)f(tak)n(e)g(the)h(follo)l(wing)g(tw)n(o)g(v)l(alues:)1162 6370 y(0)166 b(C-style)42 b(numbering)g(is)f(assumed)f(that)i(starts)f (from)h(0)1162 6613 y(1)166 b(F)n(ortran-style)42 b(numbering)g(is)f (assumed)g(that)g(starts)g(from)i(1)415 6881 y FD(ncon)406 b FK(This)47 b(is)e(used)h(to)g(specify)f(the)h(number)g(of)h(weights)e (that)h(each)f(v)n(erte)n(x)g(has.)64 b(It)46 b(is)g(also)g(the)f (number)i(of)f(balance)1162 7100 y(constraints)41 b(that)h(must)f(be)h (satis\002ed.)415 7367 y FD(nparts)286 b FK(This)54 b(is)f(used)g(to)h (specify)f(the)g(number)h(of)f(sub-domains)g(that)h(are)f(desired.)87 b(Note)53 b(that)g(the)h(number)f(of)h(sub-)1162 7587 y(domains)42 b(is)f(independent)g(of)h(the)f(number)h(of)g(processors)e (that)i(call)f(this)g(routine.)415 7854 y FD(tpwgts)277 b FK(An)52 b(array)g(of)g(size)f Fj(ncon)g FK(x)h Fj(nparts)d FK(that)j(is)g(used)f(to)h(specify)f(the)h(fraction)g(of)h(v)n(erte)n (x)d(weight)i(that)g(should)1162 8073 y(be)44 b(distrib)m(uted)g(to)g (each)f(sub-domain)h(for)h(each)e(balance)g(constraint.)58 b(If)45 b(all)f(of)g(the)g(sub-domains)f(are)h(to)g(be)g(of)1162 8292 y(the)e(same)e(size)h(for)h(e)l(v)n(ery)f(v)n(erte)n(x)f(weight,)h (then)h(each)e(of)i(the)g Fj(ncon)e FK(x)h Fj(nparts)e FK(elements)i(should)g(be)h(set)f(to)g(a)1162 8512 y(v)l(alue)c(of)g (1/)p Fj(nparts)p FK(.)47 b(If)38 b Fj(ncon)d FK(is)i(greater)f(than)h (one,)g(the)g(tar)m(get)g(sub-domain)g(weights)f(for)i(each)e (sub-domain)1162 8731 y(are)50 b(stored)g(contiguously)f(\(similar)i (to)f(the)g Fj(vwgt)e FK(array\).)76 b(Note)50 b(that)g(the)g(sum)f(of) h(all)g(of)g(the)g Fj(tpwgts)e FK(for)i(a)1162 8950 y(gi)l(v)n(e)41 b(v)n(erte)n(x)g(weight)g(should)g(be)h(one.)415 9217 y FD(ub)n(v)n(ec)336 b FK(An)42 b(array)g(of)g(size)f Fj(ncon)f FK(that)i(is)g(used)f(to)h(specify)f(the)h(imbalance)f (tolerance)g(for)i(each)e(v)n(erte)n(x)g(weight,)g(with)h(1)1162 9437 y(being)47 b(perfect)g(balance)e(and)i Fj(nparts)d FK(being)j(perfect)g(imbalance.)66 b(A)46 b(v)l(alue)g(of)h(1.05)g(for) g(each)f(of)h(the)f Fj(ncon)1162 9656 y FK(weights)41 b(is)h(recommended.)415 9923 y FD(itr)572 b FK(This)43 b(parameter)f(describes)f(the)h(ratio)h(of)g(inter)m(-processor)f (communication)g(time)h(compared)f(to)g(data)g(redistri-)1162 10142 y(b)m(ution)50 b(time.)75 b(It)50 b(should)f(be)g(set)g(between)f (0.000001)h(and)h(1000000.0.)74 b(If)50 b(ITR)g(is)f(set)g(high,)i(a)e (repartitioning)1162 10362 y(with)39 b(a)e(lo)l(w)h(edge-cut)g(will)h (be)e(computed.)50 b(If)39 b(it)f(is)g(set)g(lo)l(w)-11 b(,)38 b(a)g(repartitioning)h(that)f(requires)g(little)h(data)e (redistri-)1162 10581 y(b)m(ution)i(will)g(be)f(computed.)50 b(Good)38 b(v)l(alues)g(for)h(this)g(parameter)f(can)g(be)g(obtained)h (by)f(di)l(viding)h(inter)m(-processor)1162 10800 y(communication)j (time)g(by)f(data)g(redistrib)m(ution)h(time.)52 b(Otherwise,)40 b(a)h(v)l(alue)g(of)h(1000.0)f(is)g(recommended.)3817 11298 y(24)p eop %%Page: 25 25 25 24 bop 415 166 a FD(options)231 b FK(This)38 b(is)e(an)h(array)h(of) f(inte)n(gers)f(that)h(is)g(used)g(to)g(pass)f(additional)h(parameters) g(for)h(the)f(routine.)49 b(If)38 b Fs(options[0]=0)p FK(,)1162 385 y(then)49 b(the)g(def)n(ault)g(v)l(alues)f(are)g(used.)72 b(If)50 b Fs(options[0]=1)p FK(,)f(then)g(the)g(remaining)g(three)f (elements)g(of)h Fs(options)g FK(are)1162 604 y(interpreted)42 b(as)f(follo)l(ws:)1162 890 y(options[1])222 b(This)45 b(speci\002es)f(the)h(le)l(v)n(el)f(of)h(information)g(to)g(be)g (returned)g(during)g(the)g(e)n(x)n(ecution)e(of)i(the)g(algo-)2066 1109 y(rithm.)61 b(T)-6 b(iming)46 b(information)f(can)f(be)h(obtained) f(by)h(setting)f(this)g(to)h(1.)60 b(Additional)45 b(options)f(for)2066 1328 y(this)i(parameter)f(can)f(be)h(obtained)g(by)h(looking)f(at)g (the)g(the)g(\002le)h Fj(defs.h)d FK(in)i(the)g Fj(ParMETIS-)2066 1548 y(Lib)39 b FK(directory)-11 b(.)51 b(The)40 b(numerical)g(v)l (alues)f(there)h(should)f(be)h(added)f(to)h(obtain)g(the)g(correct)g(v) l(alue.)2066 1767 y(The)i(def)n(ault)g(v)l(alue)f(is)g(0.)1162 2019 y(options[2])222 b(This)42 b(is)f(the)h(random)g(number)f(seed)g (for)h(the)f(routine.)52 b(The)42 b(def)n(ault)f(v)l(alue)h(is)f(15.) 1162 2271 y(options[3])222 b(This)51 b(speci\002es)e(whether)i(the)f (sub-domains)g(and)g(processors)g(are)g(coupled)g(or)h(de-coupled.)77 b(If)2066 2491 y(the)47 b(number)h(of)f(sub-domains)g(desired)f(\()p Fs(i.e)p FK(.,)h Fj(nparts)p FK(\))f(and)g(the)h(number)h(of)f (processors)f(that)2066 2710 y(are)k(being)g(used)f(is)h(not)g(the)g (same,)h(then)f(these)f(must)h(be)g(de-coupled.)76 b(Ho)l(we)l(v)n(er) -7 b(,)51 b(if)f Fj(nparts)2066 2929 y FK(equals)56 b(the)g(number)g (of)h(processors,)h(these)d(can)h(either)g(be)g(coupled)f(or)i (de-coupled.)94 b(If)57 b(sub-)2066 3148 y(domains)49 b(and)g(processors)f(are)h(coupled,)h(then)f(the)g(initial)h (partitioning)g(will)g(be)e(obtained)h(im-)2066 3367 y(plicitly)66 b(from)f(the)g(graph)g(distrib)m(ution.)121 b(Ho)l(we)l(v)n(er)-7 b(,)69 b(if)c(sub-domains)f(are)h(de-coupled)f (from)2066 3587 y(processors,)44 b(then)g(the)g(initial)h(partitioning) g(needs)f(to)g(be)h(obtained)f(from)h(the)f(initial)h(v)l(alues)e(as-) 2066 3806 y(signed)j(to)h(the)f Fj(part)f FK(array)-11 b(.)66 b(A)46 b(v)l(alue)g(of)h(1)g(indicates)e(that)i(sub-domains)f (and)g(processors)f(are)2066 4025 y(coupled)50 b(and)f(2)g(indicates)g (that)g(these)g(are)g(de-coupled.)75 b(The)49 b(def)n(ault)h(v)l(alue)f (is)g(1)h(\(coupled\))g(if)2066 4244 y Fj(nparts)40 b FK(equals)g(the)i(number)g(of)f(processors)g(and)g(2)h(\(de-coupled\))f (otherwise.)415 4530 y FD(edgecut)203 b FK(Upon)51 b(successful)f (completion,)k(the)d(number)g(of)h(edges)e(that)h(are)g(cut)g(by)h(the) f(partitioning)h(is)f(written)h(to)f(this)1162 4749 y(parameter)-9 b(.)415 5034 y FD(part)443 b FK(This)33 b(is)f(an)f(array)i(of)f(size)f (equal)h(to)g(the)g(number)h(of)f(locally-stored)g(v)n(ertices.)47 b(Upon)32 b(successful)f(completion)h(the)1162 5254 y(partition)44 b(v)n(ector)e(of)h(the)g(locally-stored)g(v)n(ertices)e(is)i(written)g (to)g(this)f(array)-11 b(.)55 b(\(See)43 b(discussion)f(in)h(Section)g (4.4\).)1162 5473 y(If)i(the)f(number)g(of)h(processors)d(does)i(not)g (equal)g(the)g(number)g(of)g(sub-domains)g(and/or)g(options[3])h(is)f (set)f(to)h(2,)1162 5692 y(then)38 b(the)g(pre)l(viously)g(computed)g (partitioning)g(must)g(be)g(passed)f(to)h(the)g(routine)g(as)f(a)h (parameter)g(via)f(this)h(array)-11 b(.)415 5978 y FD(comm)314 b FK(This)45 b(is)e(a)h(pointer)g(to)g(the)g(MPI)g(communicator)h(of)f (the)g(processes)e(that)i(call)k FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)t FK(.)46 b(F)n(or)e(most)g (programs)1162 6197 y(this)e(will)g(point)g(to)f Fj(MPI)p 2607 6197 50 7 v 59 w(COMM)p 3066 6197 V 58 w(WORLD)p FK(.)3817 11298 y(25)p eop %%Page: 26 26 26 25 bop 0 166 a Ft(5.3)199 b(P)-6 b(ar)t(titioning)56 b(Re\002nement)0 471 y FB(P)-5 b(arMETIS)p 780 471 50 7 v 60 w(V3)p 1043 471 V 60 w(Re\002neKwa)m(y)43 b FK(\(idxtype)f (*vtxdist,)f(idxtype)h(*xadj,)f(idxtype)g(*adjnc)n(y)-11 b(,)41 b(idxtype)g(*vwgt,)h(idxtype)f(*adjwgt,)2072 690 y(int)h(*wgt\003ag,)f(int)h(*num\003ag,)f(int)h(*ncon,)f(int)h (*nparts,)f(\003oat)g(*tpwgts,)g(\003oat)h(*ub)n(v)n(ec,)2072 909 y(int)g(*options,)f(int)h(*edgecut,)e(idxtype)i(*part,)f(MPI)p 5112 909 V 60 w(Comm)h(*comm\))0 1299 y FB(Description)415 1518 y FK(This)i(routine)h(is)f(used)f(to)i(impro)n(v)n(e)e(the)h (quality)h(of)f(an)g(e)n(xisting)g(a)f Fy(k)10 b FK(-w)n(ay)44 b(partitioning)h(on)64 b Fy(p)49 b FK(processors)43 b(using)h(the)g (multi-)415 1738 y(le)l(v)n(el)d Fy(k)10 b FK(-w)n(ay)41 b(re\002nement)h(algorithm.)0 2061 y FB(P)-5 b(arameter)n(s)415 2272 y FD(vtxdist)268 b FK(This)39 b(array)g(describes)f(ho)l(w)g(the)h (v)n(ertices)f(of)h(the)f(graph)h(are)g(distrib)m(uted)f(among)h(the)g (processors.)49 b(\(See)39 b(discus-)1162 2491 y(sion)j(in)f(Section)h (4.1\).)51 b(Its)41 b(contents)g(are)g(identical)h(for)g(e)l(v)n(ery)f (processor)-9 b(.)415 2696 y FD(xadj,)42 b(adjncy)1162 2915 y FK(These)52 b(store)g(the)h(\(local\))f(adjacenc)n(y)f (structure)h(of)h(the)f(graph)g(at)h(each)e(processor)-9 b(.)83 b(\(See)52 b(discussion)f(in)i(Sec-)1162 3134 y(tion)42 b(4.1\).)415 3333 y FD(vwgt,)f(adjwgt)1162 3552 y FK(These)g(store)h(the)f(weights)g(of)h(the)f(v)n(ertices)g(and) g(edges.)50 b(\(See)42 b(discussion)e(in)i(Section)f(4.1\).)415 3809 y FD(ncon)406 b FK(This)47 b(is)e(used)h(to)g(specify)f(the)h (number)g(of)h(weights)e(that)h(each)f(v)n(erte)n(x)g(has.)64 b(It)46 b(is)g(also)g(the)f(number)i(of)f(balance)1162 4028 y(constraints)41 b(that)h(must)f(be)h(satis\002ed.)415 4286 y FD(nparts)286 b FK(This)54 b(is)f(used)g(to)h(specify)f(the)g (number)h(of)f(sub-domains)g(that)h(are)f(desired.)87 b(Note)53 b(that)g(the)h(number)f(of)h(sub-)1162 4505 y(domains)42 b(is)f(independent)g(of)h(the)f(number)h(of)g(processors)e (that)i(call)f(this)g(routine.)415 4762 y FD(wgt\003ag)231 b FK(This)42 b(is)f(used)g(to)h(indicate)f(if)h(the)f(graph)h(is)f (weighted.)51 b Fs(wgt\003a)n(g)42 b FK(can)f(tak)n(e)g(one)h(of)f (four)i(v)l(alues:)1162 5019 y(0)166 b(No)42 b(weights)f(\(vwgt)h(and)f (adjwgt)h(are)f(both)g(NULL\).)1162 5257 y(1)166 b(W)-13 b(eights)41 b(on)h(the)f(edges)g(only)g(\(vwgt)h(is)f(NULL\).)1162 5496 y(2)166 b(W)-13 b(eights)41 b(on)h(the)f(v)n(ertices)f(only)i (\(adjwgt)g(is)f(NULL\).)1162 5734 y(3)166 b(W)-13 b(eights)41 b(on)h(both)f(the)h(v)n(ertices)e(and)h(edges.)415 5991 y FD(num\003ag)167 b FK(This)58 b(is)f(used)g(to)h(indicate)f(the)g (numbering)h(scheme)e(that)i(is)f(used)g(for)h(the)f Fs(vtxdist)p FK(,)k Fs(xadj)p FK(,)f Fs(adjncy)p FK(,)h(and)c Fs(part)1162 6210 y FK(arrays.)51 b Fs(num\003a)n(g)42 b FK(can)f(tak)n(e)g(the)h(follo)l(wing)g(tw)n(o)g(v)l(alues:)1162 6467 y(0)166 b(C-style)42 b(numbering)g(is)f(assumed)f(that)i(starts)f (from)h(0)1162 6706 y(1)166 b(F)n(ortran-style)42 b(numbering)g(is)f (assumed)g(that)g(starts)g(from)i(1)415 6963 y FD(tpwgts)277 b FK(An)52 b(array)g(of)g(size)f Fj(ncon)g FK(x)h Fj(nparts)d FK(that)j(is)g(used)f(to)h(specify)f(the)h(fraction)g(of)h(v)n(erte)n (x)d(weight)i(that)g(should)1162 7182 y(be)44 b(distrib)m(uted)g(to)g (each)f(sub-domain)h(for)h(each)e(balance)g(constraint.)58 b(If)45 b(all)f(of)g(the)g(sub-domains)f(are)h(to)g(be)g(of)1162 7401 y(the)e(same)e(size)h(for)h(e)l(v)n(ery)f(v)n(erte)n(x)f(weight,)h (then)h(each)e(of)i(the)g Fj(ncon)e FK(x)h Fj(nparts)e FK(elements)i(should)g(be)h(set)f(to)g(a)1162 7620 y(v)l(alue)c(of)g (1/)p Fj(nparts)p FK(.)47 b(If)38 b Fj(ncon)d FK(is)i(greater)f(than)h (one,)g(the)g(tar)m(get)g(sub-domain)g(weights)f(for)i(each)e (sub-domain)1162 7839 y(are)50 b(stored)g(contiguously)f(\(similar)i (to)f(the)g Fj(vwgt)e FK(array\).)76 b(Note)50 b(that)g(the)g(sum)f(of) h(all)g(of)g(the)g Fj(tpwgts)e FK(for)i(a)1162 8059 y(gi)l(v)n(e)41 b(v)n(erte)n(x)g(weight)g(should)g(be)h(one.)415 8316 y FD(ub)n(v)n(ec)336 b FK(An)42 b(array)g(of)g(size)f Fj(ncon)f FK(that)i(is)g(used)f(to)h(specify)f(the)h(imbalance)f (tolerance)g(for)i(each)e(v)n(erte)n(x)g(weight,)g(with)h(1)1162 8535 y(being)47 b(perfect)g(balance)e(and)i Fj(nparts)d FK(being)j(perfect)g(imbalance.)66 b(A)46 b(v)l(alue)g(of)h(1.05)g(for) g(each)f(of)h(the)f Fj(ncon)1162 8754 y FK(weights)41 b(is)h(recommended.)415 9011 y FD(options)231 b FK(This)36 b(is)f(an)g(array)g(of)h(inte)n(gers)f(that)g(is)g(used)g(to)g(pass)g (parameters)f(to)i(the)f(routine.)49 b(Their)36 b(meanings)f(are)g (identical)1162 9231 y(to)42 b(those)f(of)h FA(P)-7 b(arMETIS)p 2673 9231 V 61 w(V3)p 2937 9231 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)p FK(.)415 9488 y FD(edgecut)203 b FK(Upon)51 b(successful)f (completion,)k(the)d(number)g(of)h(edges)e(that)h(are)g(cut)g(by)h(the) f(partitioning)h(is)f(written)h(to)f(this)1162 9707 y(parameter)-9 b(.)415 9964 y FD(part)443 b FK(This)33 b(is)f(an)f(array)i(of)f(size)f (equal)h(to)g(the)g(number)h(of)f(locally-stored)g(v)n(ertices.)47 b(Upon)32 b(successful)f(completion)h(the)1162 10183 y(partition)43 b(v)n(ector)d(of)i(the)g(locally-stored)f(v)n(ertices)g (is)g(written)h(to)g(this)f(array)-11 b(.)51 b(\(See)42 b(discussion)e(in)i(Section)g(4.4\).)415 10440 y FD(comm)314 b FK(This)45 b(is)e(a)h(pointer)g(to)g(the)g(MPI)g(communicator)h(of)f (the)g(processes)e(that)i(call)k FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)t FK(.)46 b(F)n(or)e(most)g (programs)1162 10660 y(this)e(will)g(point)g(to)f Fj(MPI)p 2607 10660 V 59 w(COMM)p 3066 10660 V 58 w(WORLD)p FK(.)3817 11298 y(26)p eop %%Page: 27 27 27 26 bop 0 166 a Ft(5.4)199 b(Fill-reducing)55 b(Or)l(derings)0 485 y FB(P)-5 b(arMETIS)p 780 485 50 7 v 60 w(V3)p 1043 485 V 60 w(NodeND)42 b FK(\(idxtype)g(*vtxdist,)f(idxtype)h(*xadj,)f (idxtype)g(*adjnc)n(y)-11 b(,)41 b(int)h(*num\003ag,)f(int)h(*options,) 1789 704 y(idxtype)g(*order)-7 b(,)42 b(idxtype)f(*sizes,)f(MPI)p 4172 704 V 60 w(Comm)i(*comm\))0 1222 y FB(Description)415 1441 y FK(This)g(routine)g(is)f(used)g(to)h(compute)f(a)g (\002ll-reducing)i(ordering)f(of)f(a)h(sparse)e(matrix)i(using)g (multile)l(v)n(el)f(nested)g(dissection.)0 1793 y FB(P)-5 b(arameter)n(s)415 2032 y FD(vtxdist)268 b FK(This)39 b(array)g(describes)f(ho)l(w)g(the)h(v)n(ertices)f(of)h(the)f(graph)h (are)g(distrib)m(uted)f(among)h(the)g(processors.)49 b(\(See)39 b(discus-)1162 2252 y(sion)j(in)f(Section)h(4.1\).)51 b(Its)41 b(contents)g(are)g(identical)h(for)g(e)l(v)n(ery)f(processor) -9 b(.)415 2485 y FD(xadj,)42 b(adjncy)1162 2704 y FK(These)56 b(store)h(the)f(\(local\))h(adjacenc)n(y)e(structure)i(of)g(the)f (graph)h(at)f(each)g(processor)g(\(See)h(discussion)e(in)i(Sec-)1162 2923 y(tion)42 b(4.1\).)415 3209 y FD(num\003ag)167 b FK(This)53 b(is)f(used)g(to)h(indicate)f(the)h(numbering)g(scheme)f (that)g(is)g(used)g(for)i(the)e Fs(vtxdist)p FK(,)j Fs(xadj)p FK(,)f Fs(adjncy)p FK(,)h(and)d Fs(or)-6 b(der)1162 3428 y FK(arrays.)51 b Fs(num\003a)n(g)42 b FK(can)f(tak)n(e)g(the)h(follo)l (wing)g(tw)n(o)g(v)l(alues:)1162 3714 y(0)166 b(C-style)42 b(numbering)g(is)f(assumed)f(that)i(starts)f(from)h(0)1162 3966 y(1)166 b(F)n(ortran-style)42 b(numbering)g(is)f(assumed)g(that)g (starts)g(from)i(1)415 4252 y FD(options)231 b FK(This)36 b(is)f(an)g(array)g(of)h(inte)n(gers)f(that)g(is)g(used)g(to)g(pass)g (parameters)f(to)i(the)f(routine.)49 b(Their)36 b(meanings)f(are)g (identical)1162 4471 y(to)42 b(those)f(of)h FA(P)-7 b(arMETIS)p 2673 4471 V 61 w(V3)p 2937 4471 V 60 w(P)g(ar)7 b(tKw)n(a)-5 b(y)p FK(.)415 4756 y FD(order)350 b FK(This)42 b(array)g(returns)f (the)h(result)f(of)h(the)f(ordering)h(\(described)f(in)h(Section)g (4.4\).)415 5042 y FD(sizes)423 b FK(This)51 b(array)f(returns)h(the)f (number)g(of)h(nodes)f(for)g(each)g(sub-domain)g(and)g(each)g (separator)g(\(described)f(in)i(Sec-)1162 5261 y(tion)42 b(4.4\).)415 5547 y FD(comm)314 b FK(This)45 b(is)e(a)h(pointer)g(to)g (the)g(MPI)g(communicator)h(of)f(the)g(processes)e(that)i(call)k FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)t FK(.)46 b(F)n(or)e(most)g(programs)1162 5766 y(this)e(will)g (point)g(to)f Fj(MPI)p 2607 5766 V 59 w(COMM)p 3066 5766 V 58 w(WORLD)p FK(.)0 6118 y FB(Note)415 6337 y FA(P)-7 b(arMETIS)p 1183 6337 V 61 w(V3)p 1447 6337 V 60 w(NodeND)42 b FK(requires)f(that)h(the)f(number)h(of)g(processors)e(be)i(a)f(po)l (wer)g(of)h(2.)3817 11298 y(27)p eop %%Page: 28 28 28 27 bop 0 166 a Ft(5.5)199 b(Mesh)55 b(to)g(Graph)g(T)-16 b(ranslation)0 485 y FB(P)-5 b(arMETIS)p 780 485 50 7 v 60 w(V3)p 1043 485 V 60 w(Mesh2Dual)44 b FK(\(idxtype)e(*elmdist,)f (idxtype)g(*eptr)-7 b(,)42 b(idxtype)g(*eind,)f(int)g(*num\003ag,)2011 704 y(int)h(*ncommonnodes,)e(idxtype)i(**xadj,)f(idxtype)g(**adjnc)n(y) -11 b(,)41 b(MPI)p 6043 704 V 60 w(Comm)h(*comm\))0 1222 y FB(Description)415 1441 y FK(This)e(routine)h(is)e(used)h(to)g (construct)g(a)f(distrib)m(uted)h(graph)h(gi)l(v)n(en)e(a)h(distrib)m (uted)g(mesh.)50 b(It)40 b(can)f(be)h(used)g(in)g(conjunction)g(with) 415 1660 y(other)i(routines)f(in)h(the)j FA(P)-10 b FG(A)8 b(R)g FA(M)-9 b FG(E)-34 b FA(T)g FG(I)p FA(S)48 b FK(library)-11 b(.)52 b(The)42 b(mesh)f(can)g(contain)g(elements)g(of)h(dif)l(ferent)g (types.)0 2012 y FB(P)-5 b(arameter)n(s)415 2252 y FD(elmdist)231 b FK(This)47 b(array)g(describes)e(ho)l(w)i(the)f(elements)g(of)h(the)f (mesh)h(are)f(distrib)m(uted)g(among)h(the)g(processors.)65 b(It)47 b(is)f(anal-)1162 2471 y(ogous)64 b(to)g(the)g Fj(vtxdist)d FK(array)-11 b(.)119 b(Its)64 b(contents)f(are)h (identical)g(for)g(e)l(v)n(ery)f(processor)-9 b(.)118 b(\(See)64 b(discussion)f(in)1162 2690 y(Section)42 b(4.3\).)415 2917 y FD(eptr)-15 b(,)41 b(eind)1162 3136 y FK(These)64 b(arrays)g(speci\002es)f(the)g(elements)h(that)g(are)g(stored)g (locally)g(at)g(each)f(processor)-9 b(.)118 b(\(See)64 b(discussion)f(in)1162 3355 y(Section)42 b(4.3\).)415 3641 y FD(num\003ag)167 b FK(This)52 b(is)g(used)f(to)h(indicate)f(the) h(numbering)g(scheme)f(that)h(is)f(used)h(for)g(the)g Fs(elmdist)p FK(,)h Fs(elements)p FK(,)g Fs(xadj)p FK(,)h Fs(adjncy)p FK(,)1162 3860 y(and)42 b Fs(part)f FK(arrays.)51 b Fs(num\003a)n(g)41 b FK(can)g(tak)n(e)h(one)f(of)h(tw)n(o)g(v)l (alues:)1162 4146 y(0)166 b(C-style)42 b(numbering)g(that)f(starts)g (from)h(0.)1162 4398 y(1)166 b(F)n(ortran-style)42 b(numbering)g(that)g (starts)f(from)h(1.)415 4629 y FD(ncommonnodes)1162 4848 y FK(This)i(parameter)g(determines)g(the)f(de)n(gree)g(of)i(connecti)l (vity)e(among)h(the)g(v)n(ertices)f(in)h(the)f(dual)h(graph.)58 b(Speci\002-)1162 5067 y(cally)-11 b(,)43 b(an)f(edge)g(is)h(placed)f (between)g(an)n(y)f(tw)n(o)j(elements)d(if)j(and)e(only)h(if)g(the)n(y) 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