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tiongraphwiththemaximumdegree(等于4.

Figure6.Aredistributiongraphwith(等于4.

Weneedfourmunicationstepsforthisdataredistributionsince(((G)等于((G)等于4.Inaddition,theoverallcostofthecorrespondingschedulingis38(SeeTable1).

Table1.TheschedulingcorrespondstotheedgecoloringinFigure4.

Step1(red)2(yellow)3(green)4(purple)TotalCost18631138

NotethatthetimecostofStep1(coloredinred)isdominatedbythedatasegment(with18dataelements)fromP0toQ0.Supposethatweevenlypartitionthesegmentintotwodatasegments(with9and9dataelementsrespectively)andtransmitthemindifferentsteps,thenthetimerequiredforStep1isreducedto10(dominatedbythedatasegmentfromP3toQ3).Notethatthedatapartitionaddsanedge(P0,Q0)intheoriginalredistributiongraph.Similarly,wecanpartitionanylargedatasegmentintomultiplesmalldatasegmentifthemaximumdegreeoftheresultingredistributiongraphremainsunchanging.Afterseveraldatapartitions,theoverallmunicationcostcanbereducedto29andthenumberofrequiredmunicationstepisstillminimized(seeFigure7andTable2).

Figure7.Theresultingredistributiongraphafterpartitioninglongdatasegments.

Table2.Theschedulingafterpartitionlongdatamunications.

Step1(red)2(yellow)3(green)4(purple)TotalCost995629

较正式的成果说明.

【范例】

Thealgorithmoftheselectionstepisshownasfollows.

AlgorithmSelection()

Input:AredistributiongraphG等于(S,T,E)withmaximumdegree.

Output:AredistributiongraphG等于(S,T,E(D)withmaximumdegree,whereDrepresentsthosedummyedgesaddedinthealgorithm.

Step1.Selecttheedgeek等于(si,tj)fromEsuchthatthevaluewk/(1+vk)isthelargestanddG(si)<,anddG(tj)<,,wherevkdenotesthenumberofaddeddummyedgewiththesameendpointsofek.Ifnosuchedgeexists,terminatethisalgorithm.

Step2.Addadummyedgeek'等于(si,tj)toDandsetvk等于vk+1.

Step3.GotoStep1.

ThetimeplexityofSelectionisO(mlogm),wheremisthesizeofedgesetoftheinputredistributiongraph.

4.4Complexity

5.理论上的证明(simulationresults).实验结果GEN_BLOCKdistribution.GivenanirregulararrayredistributiononA[1:N]overPprocessors,theaveragesizeofdatablocksisN/P.LetTb(Ta)denotethetotalredistributioncostwithout(with)applyingouralgorithm.ThereductionratioRequals(Tb-Ta)/Tb.Moreover,let{E1,E2,E3,等,E(}ofGdenotetheoutputofSchedulingstep.WealsodefineCi等于.Asaresult,theoverallredistributiontimeisboundedbyB等于sincetheproposedalgorithmdoesnotselectmaximum-degreeedgesforfurtherpartition.Otherwise,therequiredmunicationstepwillbeincreased.

Tothoroughlyevaluatehowouralgorithmaffectsthedatatransfercost,oursimulationsconsiderdifferentscenarios.Eachdatapointinthefollowingfiguresrepresentsanaverageofatleast10000runsineachdifferentscenario.

Thefirstscenarioassumesthatthesizeofdataarrayisfixed,i.e.,N等于100,thenumberofprocessorsrangefrom4,8,16,32,64,to128,thesizeofdatablocksisrandomlyselectedbetween1and50.InFigure12,thevalueofTbdrasticallyraisesasthenumberofprocessorsincreases.However,afterapplyingouralgorithm,theoveralldistributiontimeTasmoothlyraisesasthenumberofprocessorsincreases.NotethattheBvaluedropsasthenumberofprocessorincreaseduetothedecreaseoftheaveragevaluesofdataelementsinasinglemunication.Inshort,whenthenumberofprocessorsincreases,thereductionratioRraisesifapplyingourpartitionalgorithm.

Figure12.SimulationresultsofScenarioI.

Thesecondscenarioassumesthatthenumberofprocessorsisfixed,i.e.,P等于32,thesizeofdataarrayNequals1600,3200,6400,9600,or12800,andthesizeofdatablocksisrandomlyselectedbetween1and2((N/P).AsshowninFigure13,thevaluesofTa,Tb,andBraisesasthesizeofdataarrayNincreasesduetotheincreaseoftheaveragenumberofdataelementsinasinglemunication.However,thereductionratiostaysabout52%byapplyingourpartitionalgorithm,evenwiththelargesizeofdataarray.

Figure13.SimulationresultsofScenarioII.

结论

简单摘 要整篇论文的贡献及使用的技巧

此研究对该领域有何启发

贡献有何处可扩展

WereyourresultsexpectedIfnot,whynot

Whatgeneralizationsorclaimsareyoumakingaboutyourresults

Doyourresultscontradictorsupportotherexperimentalresults

Dotheysuggestotherobservationsorexperimentswhichcouldbedonetoconfirm,refute,orextendyourresults

Doyourresultssupportorcontradictexistingtheory

DoyourresultssuggestthatmodificationsorextensionsneedtobemadetoexistingtheoryWhatarethey

Couldyourresultsleadtoanypracticalapplications

Stresshowtheresultsinthisstudyconfirmyourengineering/Scientificmotivations(specificandgeneral)and,ultimately,yourreader'sinterests(i.e.Engineering/Scientificneed).

【范例】

Wehavepresentedaneffici

关于写文河北,写文成人的在职毕业论文范文
论文类有关论文例文
entalgorithmtoreducetheoverallredistributiontimebyapplyingdatapartition.Simulationresultsindicatesthatwhenthenumberofprocessorsorthemaximumdegreeoftheredistributiongraphincreasesortheselectedsizeofdatablocksisappropriate,ouralgorithmeffectivelyreducetheoverallredistributiontime.Infuture,wetrytoestimatethereductionratioprecisely.Wealsobelievethatthetechniquesdevelopedinthestudycanbeappliedtoresolveotherschedulingproblemsindistributionsystems.

参考文献(References)

【范例】

References:

G.BanderaandE.L.

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