Data - Parallel Implementations of Dense SimplexMethods on the Connection

We describe three data-parallel implementations of the simplex method for dense linear programming problems. The rst 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 eecient 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.