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1、LargeScaleMathwithHadoopMapReduceTsz-Wo(Nicholas)Sze,PhDHadoopSummitJune29,20111WhoamI?HortonworksSoftwareEngineerApacheHadoopPMCMemberMathematicianIInterests:FDistributedComputingFAlgorithmsFNumberTheory2AgendaIntroductionIntegerMultiplicationMapReduce-FFTMapReduce-Sum
2、MapReduce-SSAANewWorldRecordTheMachine"BehindtheComputationTsz-WoSze,HadoopSummit20113AgendaIntroductionIntegerMultiplicationMapReduce-FFTMapReduce-SumMapReduce-SSAANewWorldRecordTheMachine"BehindtheComputationTsz-WoSze,HadoopSummit20114TypicalHadoopApplicationsIMa
3、jorapplicationsofHadoopincludeSearchandcrawlingTextprocessingMachinelearning...Tsz-WoSze,HadoopSummit20115TypicalHadoopApplicationsIMajorapplicationsofHadoopincludeSearchandcrawlingTextprocessingMachinelearning...IButnotyetcommonlyusedinscienti cormathematicalapplicati
4、ons.Why?Tsz-WoSze,HadoopSummit20116WhyNotMath?INoMapReducemathlibrariesavailable,andIMorefundamentally,MapReducemathalgorithmsarenotwellstudied.Tsz-WoSze,HadoopSummit20117ExistingLibraryIReallynoMapReduceMathLibrary?Notexactly.Tsz-WoSze,HadoopSummit20118ExistingLibraryIReallyn
5、oMapReduceMathLibrary?Notexactly.IApacheMahoutAmachinelearninglibrary.Includespackagesformatrixoperations.Tsz-WoSze,HadoopSummit20119ExistingLibraryIReallynoMapReduceMathLibrary?Notexactly.IApacheMahoutAmachinelearninglibrary.Includespackagesformatrixoperations.IApacheHama
6、(Incubation)Amatrixcomputationalpackage.Tsz-WoSze,HadoopSummit201110ComputationalIntensiveProblems(1)IIntegerFactoringa.k.a.breakingRSAcryptosystem01GivenN,eandc,computemsuchthatBCBeCBcm(modN);C@AwhereNisaproductoftwoprimes.a768-bitRSAmoduluswasfactored1in20091Kleinjungeta
7、l.,Factorizationofa768-bitRSAmodulus,CRYPTO2010.Tsz-WoSze,HadoopSummit201111ComputationalIntensiveProblems(2)ISolvingPDEs(PartialDi erentialEquations)FluiddynamicsElectromagnetismFinancialanalysis...(Two-dimensionalTurbulence,courtesyofY.K.Tsang)Tsz-WoSze,HadoopSummit20111
8、2ComputationalIntensiveProblems(3)IFindingcomplexzerosofRiema
