Improved methods for storing and updating information in the out-of-kilter algorithm

Abstract

Currently, network codes based on the primal simplex algorithm are believed to be computationally superior to those based on other methods. Some modifications of the out-of-kilter algorithm of Ford and Fulkerson are given, together with proofs of their correctness and computer implementations using appropriate data structures. The computational tests in this paper indicate that the final code based on these modifications is superior to any previously implemented version of this algorithm. Although this code is not competitive with state-of-the-art primal simplex codes, its performance is encouraging, especially in the case of assignment problems.