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One-Step Algorithm for Mixed Data and Task Parallel Scheduling Without Data Replication

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(1)One-Step Algorithm for Mixed Data and Task Parallel Scheduling Without Data Replication Vincent Boudet, Frédéric Desprez, Frédéric Suter. To cite this version: Vincent Boudet, Frédéric Desprez, Frédéric Suter. One-Step Algorithm for Mixed Data and Task Parallel Scheduling Without Data Replication. [Research Report] RR-4591, LIP RR-2002-34, INRIA, LIP. 2002. �inria-00071994�. HAL Id: inria-00071994 https://hal.inria.fr/inria-00071994 Submitted on 23 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. One-Step Algorithm for Mixed Data and Task Parallel Scheduling Without Data Replication V. Boudet, F. Desprez, F. Suter. No 4591 October 2002. ISSN 0249-6399. ISRN INRIA/RR--4591--FR+ENG. ` THEME 1. apport de recherche.

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(78)        !"$#&%'() +* A11. +. + START Ai Br. Ar. x. x. A21. +. A22. −. START. −. +. B21 B22. B12. B11. −. −. +. +. Bi. x. −. A12. x. +. x. x. +. − −. x. x. +. x. +. x. x. +. − −. g0—œ‹wg{pn\4‚ª»W0ehcd¤¥‹wp ehx{XZcŸ¡qhp|1qw[ xZœ\9i³[Oe©knpn—¢i¯[‰gZžk —˜xZœ—˜|fe©kn—œqw}d:Нœ\Ÿíkl<(eh}Zz²¼Kk pnehcncd\7} zZ\7|1qw[4xyqwcd—˜k —˜qw}U¡: pn—œ‹hXUk< ¦ Cr. STOP. C11 C12. Ci. STOP C21. C22. x \1pdŸ¡qwpd[4\1z­qw}ve

(79)  ‹hpn—œz : *9<9¦ g0—œ}Še©œ˜mh«ªknXZ\)pd\7cdgZ˜k  XŠehc$k q4†\zZ—œc·k pd—œ†Zg{kn\7zjqw} k XZ\c e©[4\(‹wpd—œzjehc & ¦ @\€§Špdcdk(cd|!XZ\7z{gZœ\1z¥knXZ\7cd\^ehxZxZ˜—œ|7e©k —˜qw}Zc$qw}¯eh}vXZqw[ qw‹w\7}{\7qwgZctxZ¶e©kdŸ¡qwpn[j¦lW XZ\7} ™\­eh—œ[ \7z°ek ¬©eh˜—œzŠek —œ}{‹­k X{\­†y\7XŠef¬K—œqhp´qhŸtqhgZp ehœ‹wqhpn—˜knXZ[ ™$XZ\7} k XZ\xZœe©knŸ¡qwpd[ —˜c XZ\1kn\7pnqh‹w\7}Z\1qwgZc1¦W X{\€kµ™q"Ÿ¡qhœœqR™$—˜}Z‹4cd\7|k —œqh}Zc`xZpd\7cn\1}Ikcnqw[ \‰pn\1cngZžk clŸ¡qwp knXZ\7cd\‰kµ™q ¤K—˜}ZzZc$qhŸxZ¶eknŸ¡qwpd[4c1¦ @B?. . O O D  GD O

(80). . !. . . DGL HQP H FIFBDGF   DGL" F  . . W0eh†{œ\(]$xZpn\1cn\1}UkncšknXZ\$\iª\7|1g{k —˜qw} kn—œ[ \7c5qhŸyk X{\lqhx\1p e©kn—œqw}Zck XŠe©kN|1qw[ xqwcd\ k XZ\/f u›u eh}Zz¹¼Uk p e©cncn\1}+k!e©cn¤¯‹wpnehxZXZc1¦ Neh|!X²[4e©k pd—ži¯—˜}I¬wqwž¬w\7z@—œ}¥k XZ\1cn\4|7qw[ xZg{k e©k —˜qw}Zc—œcqhŸ cn!— `1\    ¦ W0e©†Zœ\v‡¥x{pn\7cd\7}Ik c"knp eh}{cdŸ¡\7p^k —˜[4\1c^qhŸe    [4e©k pd—ži †\kµ™\1\7}­knXZ\|7qw}{cn—œz{\7pn\1zv|1qw}{§Š‹wg{p e©kn—œqw}Zc1¦ .       0    . )(  4 * )(        4      *      . 5o pnqKzZgZ|1k  zZzZ—˜kn—œqw} W0eh†{œ\]w» 0iª\7|1g{k —˜qw}Ok —˜[4\1cNqhŸ®k X{\tqwxy\7pÛ± Wy† \1ehkµ†Z™š˜\`\7\1‡ª}­»ñk alX{\1\zZ|1—œc·qwk }{pn§Š—˜†Z‹hg{gZknp —œe©qwkn}^—œqw|7}{qhc7cd¦ k e)[Oe©knpn—¢i e©k —˜qw}Zc=gZcd\7z­—œ} f u›u eh}Zzv¼Kk pnehcncd\7}®¦ . hih Aì jlk^mlno.

(81) ][. (6+" "   time 0,11s Redistribution of Tmp4 Cr = Tmp1−Tmp2 0,11s Redistribution of Tmp2 Ci = Tmp3+Tmp4. Tmp3 = Ai x Br. Tmp4 = Ar x Bi. Redistribution of Ar Redistribution of Ai Tmp1 = Ar x Br Tmp2 = Ai x Bi. Redistribution of Ai Redistribution of Br 4. g0—˜‹wgZpd\_[{»Bu­—žiª\1zª±µxŠe©p eh˜œ\7ycn|!X{\7zZgZ˜\Ÿ¡qhp=k XZ\ef u›u@¦ 0. 8. g—œ‹wgZpd>\ [‰cnX{qs™$c knXZ\(cn|!XZ\1zZgZ˜\)xZpdqªz{gZ|7\1zj†ImqhgZp eh˜‹wqwpn—žk XZ[ Ÿ¡qwpšk XZ

(82) \ f u›u³¦ gºqhp pn\fe©zŠeh†Z—˜œ—˜kµm^pd\fehcdqw}Zc1«{™\tzZq´}Zqhk XZeR¬h\(pn\1cnxy\7|1kn\7zk X{\`cn|7ehœ\`†y\1kµ™š\7\1}jk ehcn¤Uc1¦„`}OknXZ\ qhk XZ\1p5XŠeh}Zz^k X{\ cnXŠehz{\7zOxZehpdknc5pn\7x{pn\7cd\7}IkknXZ\ —œz{œ\kn—œ[ \=qhŸEe|1qw}{§Š‹hgZp e©kn—œqw}E¦ @\l|7eh} cn\7\^k XZe©k€x{pnqKzZgZ|1knc€e©pn\ x\1pdŸ¡qwpd[4\1z@†Im¥xŠeh—˜p7«.™$XZ—˜œ\ ehzZzZ—žk —˜qw}³eh}Zz+cdgZ†{knp eh|k —œqh}+ehpd\ |7qw[ xZg{kn\7zcn\1pn—¶e©œ˜m qw} )( ¦5W X{—œc$ehcdcn—œ‹h}Z[4\1}Ik$|7qw[ \7c=Ÿ¡pdqw[knXZ\(ŸÐeh|1kk XŠe©k knXZ\7cd\(kµ™q k!ehcd¤KclxZpdqªzZg{|7\(k \1pn[ —œ}ŠehzŠe©k e{A¦ gºg{pdk X{\7pn[ qwpd\`k XZ—˜c cnqw˜g{k —˜qw}—œc ˜\7cnc$\9i{xy\7}{cn—˜¬h\)knXŠeh} ehœ—˜‹w}Z—œ}{‹‰[Oek pn—˜|7\1clqh} *4«xy\7p·Ÿ¡qwpn[ —œ}Z‹‰knXZ\€qhx\1p e©kn—œqw}jeh}Zzjk XZ\1}vpd\7zZ—˜cdk pd—œ†Zgªk —œ}{‹^knXZ\ pn\7cdgZ˜k7¦ g—œ‹wgZpd\ ]›cnXZqR™$c´k X{\cn|!XZ\1zZgZœ\jxZpdqªzZg{|7\7z°†Im¹qwg{p^ehœ‹wqhpn—˜knXZ[ Ÿ¡qwp€knXZ\cdknp ehcdcn\7} zZ\7|1qw[4xyqwcd—˜k —˜qw}®¦ +\)|feh}›cd\7\k XŠe©ktehzZz{—˜k —˜qw}Zclehpd\)[4ehxZxy\7z­|7œqhcn\k q4knXZ\€zZe©k!e^k XZ\m —œ}I¬wqwž¬w\©¦0W XZ\B§Špnc·kñcn—¢ixZpnqKzZgZ|k c0ehpn\š|7qw[ xZg{kn\7z€xZeh—œp·™$—œcn\©«hgZcd—œ}Z‹ [4—¢iª\7zª±äxŠehp e©œœ\1œ—˜cn[j¦ W XZ\Ocd\1¬w\1}Ik X eh}Zz²œehcdk)xZpdqªzZg{|1k)—œc\iª\7|1g{k \1z qh}@k X{\4™$XZqw˜\Ocd\1k‰q©Ÿ xZpnqK|7\1cncdqwpnc1«Nehc k XZ\1pn\zZqK\7c^}Zqhk^pd\7[4eh—œ}°eh}I m µœqw}{‹ Ok ehcn¤@k q¥cn|!XZ\1zZgZ˜\­—˜} xZehp eh˜œ\1qhŸ —˜k7¦°u­—žiª\1zª± xŠehp e©œœ\1œ—˜cn[<e©œcnqOehxZxy\fehpdc`—œ}jk XZ\€\iª\7|1g{k —˜qw}¯qhŸ5k X{\‰ehzZz{—˜k —˜qw}Zcl}Z\7\1zZ\7z¯knq"|7qw[ xZg{kn\ )( ( eh}Zz  4 4 ¦ g0—œ}ZehœžmOk X{\Ÿ¡qwg{p œehcdk ehzZz{—˜k —˜qw}Zc ™$XZ—˜|!X›xZpnqKzZgZ|1\kn\7pd[4—˜}Šeh.zŠe©k eOehpd\ x\1pdŸ¡qwpd[4\1zjqh} )( ¦ Weh†Z˜\ ,xZpd\7cd\7}Ik cknXZ\$‹Ieh—˜}4e©|!XZ—œ\¬w\7zO†Um^cd|!XZ\7z{gZœ\1c=xZpnqKzZgZ|1\7z4†Um^qhgZpBehœ‹wqhpn—˜knXZ[ qs¬h\7p(zŠek!e±äxŠehp e©œœ\1.cn|!XZ\1zZgZ˜\7c7¦W XZ\‰z{\7|7pd\fehcd\^|feh}¯†y\‰\iªxZœeh—œ}{\7z›†ImvknXZ\‰\¬wqw˜g{k —˜qw} qhŸñk X{\‰\iª\7|1g{k —˜qw}›k —˜[4\qhŸBe4xZpnqKzZgZ|k`pn\1cnxy\7|k —˜¬h\7žmvqw}veh}Zz *4xZpnqK|7\1cncnqhpnc7¦ XZ\7} [Oe©knpn—˜|7\7cN‹w\k=œehpn‹w\©«wk XZ\ p e©kn—œq†\kµ™\1\7}"knXZ\7cd\tk —˜[4\1cNkn\7}Zz{ck qR™ehpnzZcBkµ™q{¦5W XZ\ kn—œ[ \ . ë-,ih.ë-..

(83) 

(84)        !"$#&%'() +*. time 0,11s C22 Redistribution of U4 0,11s C12 Redistribution of Q5 0,11s C21 Redistribution of Q2 0,11s C11 Redistribution of U2 U3 U2 Redistribution of Q5 Redistribution of Q7 U1 U4 Redistribution of Q4 Q7 Redistribution of T5 and T10 Q5 Q6 Exchange of T4 and B22 Q3 Q4 Exchange of T7 and A22 Q1 Q2 Exchange of T2 and T6 T10 T5 T9 T4 T8 T3 T7 T2 T6 T1 0 4 8. g0—˜‹wgZpn\>]ª»Bu­—žiª\1zª±µxŠe©p eh˜œ\7cn|!XZ\1zZgZ˜\Ÿ¡qwpl¼Uk p e©cncn\1}vzZ\1|7qw[ xyqwcn—žk —œqh}®¦. hih Aì jlk^mlno. ]].

(85) ])*. (6+" "  . ]RˆI‡© ‡hˆh * ,wˆ0]w‡ Iˆwƒ2[ f u›u ]f ƒ ± *{¦ , ¼Kknp ehcdcn\1} 3‡ ,{¦ ] ]s‚ ] ] ± W0e©†Zœ\_,{» beh—œ}{c=qhŸ[4—¢i{\1zª±µxZehp eh˜œ\1cd|!XZ\7zZg{œ\7clqR¬w\1p zŠek!e±äxŠehp e©œœ\1qh}Z\7c1¦ Z} \7\1zZ\7z¥k q|1qw[4x{g{k \€kµ™šqxZpnqKzZgZ|k c(gZcd—œ}Z‹[ —žiª\1zª±µxŠe©p eh˜œ\7˜—œcd[ k XUgZc`kn\7}Zz{cknqR™=ehpdzZc k XZ\(k —˜[4\ k q^cn\1pn—¶e©œ˜m4\iª\1|7g{kn\knXZ\c eh[ \qwx\1p e©kn—œqw}{c=gZcn—˜}Z‹^zŠe©k e±µxŠe©p eh˜œ\7˜—œcd[­¦ @. . D$JD&P O D  GD O"! . . . DGL. . HQP H FIFIDGF.    DGL" F  . . tc€[ \7}Ikn—œqw}Z\1z+†y\1Ÿ¡qwpd\h«}Zq›ehcdcngZ[ x{kn—œqw}@XŠehc€†y\7\1}²[4ehzZ\4eh†qhg{k)knXZ\ XZqw[ qw‹w\7}{\7—˜kµm. hq ŸknXZ\^\iª\7|1g{k —˜qw}+xZœe©knŸ¡qhpn[¸z{gZpn—˜}Z‹jknXZ\^zZ\7cd—œ‹w}³qhŸqwgZpehœ‹hqwpn—žk XZ[j¦ +\^cd|!XZ\7zZg{œ\7z k XZ\¼Kknp ehcdcn\1}jz{\7|7qh[4xyqwcn—žk —˜qw}"qw}e‰XZ\k \1pnqw‹w\1}Z\7qhgZc$xZ¶e©kdŸ¡qwpn[~|1qw[4xyqwcd\7zqhŸ kµ™šq X{q©± [4qw‹h\7}Z\1qwgZc |7œg{cdk \1pnc qhŸ(zZ— E\1pn\1}Uk4xZpdqª|1\7cncd—œ}Z‹@cnxy\7\1zZcO|1qw}Z}Z\1|1k \1z k XZpdqwgZ‹wX£e gºehc·k 5knXZ\7pd}Z\1k=œ—œ}{¤y¦ñÅt\7}Zq©k \ )( e©ck XZ

(86) \ ÛcdœqR™  |7qw}{§Z‹wgZp ek —œqh}®«  4 ehcšknXZ\ µŸÐe©cdk l|1qw}{§Š‹hgª± p e©kn—œqw}´e©}Zz * ehcñk X{\=™$XZqwœ\ cd\1kNqhŸxZpdqª|1\7cncdqwpnc1¦Buve©knpn—œ|1\7c & e©}Zz ) e©pn\ pn\1cnxy\7|k —˜¬h\7žm zZ—œc·k pn—˜†Zg{kn\7zqw} )( e©}Zz  4 ¦ Weh†Z˜\¹•x{pn\7cd\7}Ik c¥k X{\ \9iª\7|7gªk —œqh} kn—œ[ \7c¯qhŸ k XZ\°qwxy\7pne©k —˜qw}Zc›|1qw[ xqwcd—œ}Z‹ knXZ\ ¼Kk pnehcncd\7}°k!ehcd¤²‹wp e©xZX®¦ Neh|!X [Oek pn—¢i@—œ}I¬wqwž¬w\1z–—˜}²k XZ\1cn\|7qw[ xZg{k e©k —˜qw}Zc‰—˜c´qhŸ cn!— `1\      ¦ñWeh†Z˜\‚€xZpn\1cn\1}Uknc k p e©}ZcdŸ¡\1p=k —œ[ \7cšqhŸe      [4e©k pd—ži4†y\1kµ™š\7\7} k XZ\|7qh}Zcn—˜zZ\7pd\7zj|7qw}{§Z‹wgZp ek —œqh}Zc7¦ . . ) (  4 *              . )(  4 * )(         4       *     . 5o pdqªzZg{—˜k  zZzZ—žk —œqh} W0eh†{œ\$Z» 0iª\7|1g{k —˜qw}Ok —˜[4\1cNqhŸ®k X{\tqwxy\7pÛ± W†y\1ehkµ†Z™š˜\`\7\1‚ª}­»ñk alX{\1\zZ|1—œc·qwk }{pn§Š—˜†Z‹hg{gZknp —œe©qwkn}^—œqw|7}{qhc7cd¦ k e)[Oe©knpn—¢i e©k —˜qw}Zc=gZcd\7z­—œ}­¼Kk pnehcncd\7}®¦ @\|feh}cd\7\(k XŠekle^zZe©k!e±äxŠehpnehœ˜\7ycn|!XZ\1zZgZœ\(™$—˜œ®e©|!XZ—œ\¬w\xqKqwp=xy\7p·Ÿ¡qwpn[4eh}Z|1\(qw} cngZ|!X+ejxZœe©knŸ¡qhpn[j¦ ” }ZzZ\7\1z+k X{\ kn—œ[ \€k qj|7qw[ xZg{kn\ ejxZpdqªz{gZ|1k)qw}¥k XZ\´™$XZqw˜\^cn\1k)qhŸ xZpnqK|7\1cncnqhpnc=—˜cš[ qwpn\$k XZeh}OŸ¡qwgZpNk —˜[4\1cš†{—œ‹w‹w\1pBknXŠeh}OknXZ\t\9iª\7|7gªk —œqh}Ok —˜[4\ eh|!XZ—˜\1¬w\1zqw} k XZ\(ŸÐehc·k$|7qw}{§Z‹wgZp ek —œqh}®¦ . ë-,ih.ë-..

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