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PERMUTING SPARSE RECTANGULAR MATRICES INTO BLOCK-DIAGONAL FORM
 

Summary: PERMUTING SPARSE RECTANGULAR MATRICES
INTO BLOCK-DIAGONAL FORM
CEVDET AYKANAT, ALI PINAR, AND ¨UMIT V. C¸ATALY¨UREK§
SIAM J. SCI. COMPUT. c 2004 Society for Industrial and Applied Mathematics
Vol. 25, No. 6, pp. 1860­1879
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.
Key words. coarse-grain parallelism, sparse rectangular matrices, singly bordered block-
diagonal form, doubly bordered block-diagonal form, graph partitioning by vertex separator, hy-
pergraph partitioning
AMS subject classifications. 65F05, 65F50, 65F20, 65K05, 65Y05, 05C50, 05C65, 05C85,
05C90
DOI. 10.1137/S1064827502401953
1. Introduction. Block-diagonal structure of sparse matrices has been exploited

  

Source: Aykanat, Cevdet - Department of Computer Engineering, Bilkent University

 

Collections: Computer Technologies and Information Sciences