Sparse matrix ordering with Scotch
Finding good orderings is a critical issue for the efficient factorization of sparse symmetric matrices, both in terms of space usage and solution time. Several ordering techniques have been proposed, among which nested dissection is gaining increasing popularity, due to its suitability for parallel solving.
This paper presents the sparse matrix ordering capabilities of Scotch, a software package for static mapping, graph partitioning, and sparse matrix ordering. Scotch uses nested dissection ordering, and computes small vertex separators from edge separators by computing minimum covers on the bipartite graphs associated with the edge-cuts.
We give brief descriptions of our implementation of nested dissection and of the separation and ordering methods that it uses, and compare its performance to other ordering programs.
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