A linear reordering algorithm for parallel pivoting of chordal graphs
SIAM Journal on Discrete Mathematics
A fast algorithm for reordering sparse matrices for parallel factorization
SIAM Journal on Scientific and Statistical Computing
Parallel algorithms for sparse linear systems
SIAM Review
Highly parallel sparse Cholesky factorization
SIAM Journal on Scientific and Statistical Computing
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
On finding minimum-diameter clique trees
Nordic Journal of Computing
Orderings for Parallel Sparse Symmetric Factorization
Proceedings of the Third SIAM Conference on Parallel Processing for Scientific Computing
On Optimal Fill-Preserving Orderings of Sparse Matrices for Parallel Cholesky Factorizations
IPDPS '00 Proceedings of the 14th International Symposium on Parallel and Distributed Processing
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In this paper, we consider the problem of finding fill-preserving sparse matrix orderings for parallel factorization. That is, given a large sparse symmetric and positive definite matrix A that has been ordered by some fill-reducing ordering, we want to determine a reordering that is appropriate in terms of preserving the sparsity and minimizing the cost to perform the Cholesky factorization in parallel. Past researches on this problem all are based on the elimination tree model, in which each node represents the task for factoring a column, and thus, can be seen as a coarse-grained task dependence model. To exploit more parallelism, Joseph Liu proposed a medium-grained task model, called the column task graph, and showed that it is amenable to the shared-memory supercomputers. Based on the column task graph, we devise a greedy reordering algorithm, and show that our algorithm can find the optimal ordering among the class of all fill-preserving orderings of the given sparse matrix A.