A recursive bipartitioning algorithm for permuting sparse square matrices into block diagonal form with overlap

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buir.contributor.authorAykanat, Cevdet
dc.citation.epageC121en_US
dc.citation.issueNumber1en_US
dc.citation.spageC99en_US
dc.citation.volumeNumber35en_US
dc.contributor.authorAcer, S.en_US
dc.contributor.authorKayaaslan, E.en_US
dc.contributor.authorAykanat, Cevdeten_US
dc.date.accessioned2016-02-08T09:39:21Z
dc.date.available2016-02-08T09:39:21Z
dc.date.issued2013en_US
dc.departmentDepartment of Computer Engineeringen_US
dc.description.abstractWe investigate the problem of symmetrically permuting a square sparse matrix into a block diagonal form with overlap. This permutation problem arises in the parallelization of an explicit formulation of the multiplicative Schwarz preconditioner and a more recent block overlapping banded linear solver as well as its application to general sparse linear systems. In order to formulate this permutation problem as a graph theoretical problem, we define a constrained version of the multiway graph partitioning by vertex separator (GPVS) problem, which is referred to as the ordered GPVS (oGPVS) problem. However, existing graph partitioning tools are unable to solve the oGPVS problem. So, we also show how the recursive bipartitioning framework can be utilized for solving the oGPVS problem. For this purpose, we propose a left-to-right bipartitioning approach together with a novel vertex fixation scheme so that existing 2-way GPVS tools that support fixed vertices can be effectively and efficiently utilized in the recursive bipartitioning framework. Experimental results on a wide range of matrices confirm the validity of the proposed approach. © 2013 Society for Industrial and Applied Mathematics.en_US
dc.identifier.doi10.1137/120861242en_US
dc.identifier.issn1064-8275
dc.identifier.urihttp://hdl.handle.net/11693/21000
dc.language.isoEnglishen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/120861242en_US
dc.source.titleSIAM Journal on Scientific Computingen_US
dc.subjectBlock diagonal form with overlapen_US
dc.subjectCombinatorial scientific computingen_US
dc.subjectGraph partitioning by vertex separatoren_US
dc.subjectPartitioning with fixed verticesen_US
dc.subjectRecursive bipartitioningen_US
dc.subjectSparse square matricesen_US
dc.subjectBlock diagonalen_US
dc.titleA recursive bipartitioning algorithm for permuting sparse square matrices into block diagonal form with overlapen_US
dc.typeArticleen_US

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