Data-Parallel Implementations of Dense Simplex Methods on the Connection Machine CM-2

Abstract

We describe three data-parallel implementations of the simplex method for dense linear programming problems. The first implementation uses a full tableau and the most-negative reduced cost pivot rule, the second uses a tableau and the steepest-edge pivot rule, and the third is a revised method with explicit inverse. All are implemented on a Connection Machine CM-2 massively parallel computer system, using a variant of Fortran 90. Using special data structures called stripe arrays, we produce efficient implementations. We compare the implementations to one another and to MINOS 5.4 on a Sun workstation. Test problems are from NETLIB, supplemented by a few additional, genuinely dense models from real applications. An appendix also gives recent results on the Connection Machine CM-5. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.