A parallelization of the simplex method

This paper presents a parallelization of the simplex method for linear programming. Current implementations of the simplex method on sequential computers are based on a triangular factorization of the inverse of the current basis. An alternative decomposition designed for parallel computation, called the quadrant interlocking factorization, has previously been proposed for solving linear systems of equations. This research presents the theoretical justification and algorithms required to implement this factorization in a simplex-based linear programming system.