 
Summary: PERMUTING SPARSE RECTANGULAR MATRICES
INTO BLOCKDIAGONAL 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. Blockdiagonal 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 stateoftheart 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. coarsegrain parallelism, sparse rectangular matrices, singly bordered block
diagonal form, doubly bordered blockdiagonal 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. Blockdiagonal structure of sparse matrices has been exploited
