A Subtree-Partitioning Algorithm for Inducing Parallelism in Network Simplex Dual Updates

Abstract

This paper reports on the development of a very efficient method for partitioning the network simplex basis subtree in which dual values must be updated during a pivot. The partitioning procedure may be concurrently executed by multiple processes. The resulting rapid decomposition of the subtree allows an arbitrary number of processes to be utilized in the actual dual update. This approach alleviates a primary limitation of the most efficient parallel network simplex implementation published to date. The new code performs at least as well as the previous implementation on medium-scale problems and reduces average solution time by over 34% on large-scale problems.