Permuting Sparse Rectangular Matrices into Block-Diagonal Form

Authors:
Cevdet Aykanat;Ali Pinar;Ümit V. Çatalyürek
Affiliations:
-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2004

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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.