Reordering sparse matrices for parallel elimination

Abstract We consider the problem of finding equivalent reorderings of a sparse matrix so that the reordered matrix is suitable for parallel Gaussian elimination. The elimination tree structure is used as our parallel model. We show that the reordering scheme by Jess and Kees generates an elimination tree with minimum height among all such trees from the class of equivalent reorderings. A new height-reducing algorithm based on elimination tree rotation is also introduced. Experimental results are provided to compare these two approaches. The new reordering algorithm using rotation is shown to produce trees with minimum or near-minimum height. Yet, it requires significantly less reordering time.

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