Parallel computing for network optimization: a cluster-based approach for the dual transshipment problem

Abstract

The traditional simplex method for solving the transshipment problem or its dual does not offer much scope for parallelization because it moves from one basic solution to another. To address this problem, we recently presented a new method called the Modified Network Dual Simplex method. This method incorporates two novel features: a technique to convert a non-basic dual feasible solution to a basic dual feasible solution, and strategies for performing pivots concurrently. In a more recent paper (1994), theauthors discuss the suitability of this approach in the Integrated VLSI layout compaction and wire balancing problem. In this paper, we describe another novel method for solving the dual transshipment problem. It combines the concurrent pivoting strategies of with a massively parallel method for converting a non-basic feasible solution to a basic feasible solution (without reducing the objective value). The method employs extensively the notion of cluster firing. Results of testing of this method on large scale graphs are also presented.