Parmetis parallel graph partitioning and sparse matrix ordering library

Graphpartitioninghasbeenshown to beaneffective way to divide a largecomputationover an arbitrarynumber of processors.A goodpartitioningcanensureload balanceandminimize the communicationoverheadof the computationby partitioningan irregularmeshinto p equalpartswhile minimizing thenumberof edgescut by the partition. For a largeclassof irregularmeshapplications,thestructureof thegraphchangesfrom onephaseof the computationto thenext. Eventually, asthegraphevolves,theadaptedmeshhasto berepartitionedto ensuregood loadbalance.Failureto do sowill leadto higherparallelrun time. This repartitioningneedsto maintaina low edgecut in orderto minimizecommunicationoverheadin thefollow-on computation.It alsoneedsto minimizethetime for physicallymigratingdatafrom oneprocessorto anothersincethis time candominateoverall run time. Finally, it mustbefastandscalablesinceit maybenecessaryto repartitionfrequently. Partitioningtheadaptedmeshagain from scratchwith an existing graphpartitionercanbe donequickly andwill result in a low edge-cut.However, it will leadto anexcessi ve migrationof dataamongprocessors.In this paper , we presentnew parallelalgorithmsfor robustlycomputingrepartitioningsof adapti vely refinedmeshes.Thesealgorithmsperformdiffusionof verticesin a multilevel framework andminimizedatamovementwithout compromisingtheedge-cut.Furthermore,our parallel repartitionersincludeparameterizedheuristicsto specificallyoptimizeedge-cut,totaldatamigration,or themaximum amountof datamigratedinto andoutof any oneprocessor . Our resultsonavarietyof syntheticmeshesshow thatour parallelmultilevel diffusionalgorithmsarehighly robustschemesfor repartitioningadapti ve meshes.Theresulting edge-cutsarecloseto thoseresultingfrom partitioningfrom scratchwith a state-of-the-art graphpartitioner , while datamigrationis substantiallyreduced.Furthermore,repartitioningcanbe donevery fast. Our experimentsshow thatmesheswith aroundeightmillion verticescanberepartitionedona256-processor CrayT3D in only acoupleof seconds.