Permuting sparse rectangular matrices into block-diagonal form

Date
2004
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Source Title
SIAM Journal on Scientific Computing
Print ISSN
1064-8275
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Publisher
SIAM
Volume
25
Issue
6
Pages
1860 - 1879
Language
English
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Abstract

We investigate the problem of permuting a sparse rectangular matrix into block-diagonal form. Block-diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization, and QR factorization. To represent the nonzero structure of a matrix, we propose bipartite graph and hypergraph models that reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Our experiments on a wide range of matrices, using the state-of-the-art graph and hypergraph partitioning tools MeTiS and PaToH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and runtime.

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Published Version (Please cite this version)