Many optimization algorithms involve repeated processing of a fixed set of linear constraints. If the constraint matrix A is pre-processed to be sparser, then algebraic operations on A will become faster. The paper considers the problem of making a given matrix as sparse as possible, the Sparsity Problem (SP). In a companion paper with S. Frank Chang, some theoretical algorithms for SP were developed under a non-degeneracy assumption. Here the paper investigates what must be done to make those algorithms applicable in practice. It reports encouraging computational results in making linear programming constraint matrices sparser. The paper also finds that the Simplex Algorithm can solve the reduced LPs faster. Comparisons are made to a heuristic algorithm for SP of Adler et al.
