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

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.