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Abstract
Abstract.Anexactsolutionmethodforthegraphbisectionproblemispresented.Wedescribeabranch-and-boundalgorithmwhichisbasedonacuttingplaneapproachcombiningsemideniteprogrammingandpolyhedralrelax- forvariousclassesofgraphs.Theresultsindicatethatthepresentapproach ations.Wereportonextensivenumericalexperimentswhichwereperformed isparticularlywellsuitedforspecialclassesofgraphsasplanargraphsand time,andprovidestightapproximationsforlargerinstances.Ourapproach solvesgeneralprobleminstanceswith80�90verticesexactlyinreasonable graphsbasedongridstructures. vertexsetconsistingofnvertices,andEtheedgeset.Theweightoftheedgesare nents.Givenisanundirectededge-weightedgraphG(V;E),whereVdenotestheWeconsidertheproblemofpartitioningtheverticesofagraphintotwocompo-ofthegraphbyL:=Diag(Aen)�A.Here,enisthen-vectorofallonesandthe givenbytheLaplacematrixL,whichisdenedthroughtheadjacencymatrixA edgesaresaidtobecutbythepartition.Weassumethatn1n2anddenoteby totalweightoftheedgeshavingonevertexinV1andoneinV2isminimized.These
