Implementation and computational results for the hierarchical algorithm for making sparse matrices sparser

Authors:
S. Frank Chang;S. Thomas McCormick
Affiliations:
GTE Labs, Waltham, MA;Univ. of British Columbia, Vancouver, B.C., Canada
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
1993

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Increasing sparsity in matrices for large-scale optimization--theoretical properties and implementational aspects

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Abstract

If A is the (sparse) coefficient matrix of linear-equality constraints, for what nonsingular T is A = TA as sparse as possible, and how can it be efficiently computed? An efficient algorithm for this Sparsity Problem (SP) would be a valuable preprocessor for linearly constrained optimization problems. In a companion paper we developed a two-pass approach to solve SP called the Hierarchical Algorithm. In this paper we report on how we implemented the Hierarchical Algorithm into a code called HASP, and our computational experience in testing HASP on the NETLIB linear-programming problems. We found that HASP substantially outperformed a previous code for SP and that it produced a net savings in optimization time on the NETLIB problems. The results allow us to give guidelines for its use in practice.