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dc.contributor.authorÇatalyürek, Ü. V.en_US
dc.contributor.authorAykanat, Cevdeten_US
dc.contributor.authorKayaaslan, E.en_US
dc.date.accessioned2016-02-08T09:51:00Z
dc.date.available2016-02-08T09:51:00Z
dc.date.issued2011en_US
dc.identifier.issn1064-8275
dc.identifier.urihttp://hdl.handle.net/11693/21776
dc.description.abstractA typical first step of a direct solver for the lin ear system Mx = b is reordering of the symmetric matrix M to improve execution time and space requirements of the solution process. In this work, we propose a novel nested-dissection-based ordering approach that utilizes hypergraph partitioning. Our approach is based on the formulation of graph partitioning by vertex separator (GPVS) problem as a hypergraph partitioning problem. This new formulation is immune to deficiency of GPVS in a multilevel framework and hence enables better orderings. In matrix terms, our method relies on the existence of a structural factorization of the input M matrix in the form of M = AA T (or M = AD2AT). We show that the partitioning of the row-net hypergraph representation of the rectangular matrix A induces a GPVS of the standard graph representation of matrix M. In the absence of such factorization, we also propose simple, yet effective structural factorization techniques that are based on finding an edge clique cover of the standard graph representation of matrix M, and hence applicable to any arbitrary symmetric matrix M. Our experimental evaluation has shown that the proposed method achieves better ordering in comparison to state-of-the-art graph-based ordering tools even for symmetric matrices where structural M = AAT factorization is not provided as an input. For matrices coming from linear programming problems, our method enables even faster and better orderings. © 2011 Societ y for Industrial and Applied Mathematics.en_US
dc.language.isoEnglishen_US
dc.source.titleSIAM Journal on Scientific Computingen_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/090757575en_US
dc.subjectCombinatorial scientific computingen_US
dc.subjectFill - reducing orderingen_US
dc.subjectHypergraph partitioningen_US
dc.subjectClique coveren_US
dc.titleHypergraph partitioning-based fill-reducing ordering for symmetric matricesen_US
dc.typeArticleen_US
dc.departmentDepartment of Computer Engineeringen_US
dc.citation.spage1996en_US
dc.citation.epage2023en_US
dc.citation.volumeNumber33en_US
dc.citation.issueNumber4en_US
dc.identifier.doi10.1137/090757575en_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.contributor.bilkentauthorAykanat, Cevdet
dc.identifier.eissn1095-7197


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