Permuting sparse rectangular matrices into block-diagonal form
This work investigates the problem of permuting a sparse rectangular matrix into block diagonal form. Block diagonal form of a matrix grants an inherent parallelism for the solution of the deriving problem, as recently investigated in the context of mathematical programming, LU factorization and QR factorization. We propose graph and hypergraph models to represent the nonzero structure of a matrix, which reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Besides proposing the models to represent sparse matrices and investigating related combinatorial problems, we provide a detailed survey of relevant literature to bridge the gap between different societies, investigate existing techniques for partitioning and propose new ones, and finally present a thorough empirical study of these techniques. Our experiments on a wide range of matrices, using state-of-the-art graph and hypergraph partitioning tools MeTiS and PaT oH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and run time.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- USDOE Director, Office of Science (US)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 826102
- Report Number(s):
- LBNL-51866; R&D Project: 365968; TRN: US200424%%441
- Journal Information:
- SIAM Journal on Scientific Computing, Vol. 25, Issue 6; Other Information: Journal Publication Date: 2004; PBD: 9 Dec 2002; ISSN 1064-8275
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
FACTORIZATION
MATRICES
PROGRAMMING
COARSE-GRAIN PARALLELISM SPARSE RECTANGULAR MATRICES SINGLY-BORDERED BLOCK-DIAGONAL FORM DOUBLY-BORDERED BLOCK-DIAGONAL FORM GRAPH PARTITIONING BY VERTEX SEPARATOR HYPERGRAPH PARTITIONING.