A fast algorithm for reordering sparse matrices for parallel factorization
- Boeing Computer Services, Seattle, WA (US)
- Dept. of Computer Science, Pennsylvania State Univ., University Park, PA (US)
This paper reports on a fast algorithm for reordering sparse matrices for parallel factorization. The parallel ordering is computed in two steps. First, the matrix A is ordered by some fill-reducing ordering. Second, a parallel ordering of A is computed from the filled graph that results from symbolically factoring A using the initial fill-reducing ordering. Among all orderings whose fill lies in the filled graph, this parallel ordering achieves the minimum number of parallel steps in the factorization and does not specify the implementation details of an algorithm for either step of this scheme. a new fast algorithm that implements the parallel ordering step by exploiting the clique tree representation of a chordal graph is presented. The cost of the parallel ordering step is reduced well below that of the fill-reducing step. This algorithm has time and space complexity linear in the number of compressed subscripts for L. i.e., the sum of the sizes of the maximal cliques of the filled graph. Running times nearly identical to Kiu's heuristic composite rotations algorithm, which approximates the minimum number of parallel steps, are demonstrated empirically.
- Sponsoring Organization:
- National Science Foundation (NSF); National Science Foundation, Washington, DC (United States)
- OSTI ID:
- 5608339
- Journal Information:
- SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States), Vol. 10:6; ISSN 0196-5204
- Country of Publication:
- United States
- Language:
- English
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