Parallel approaches to the solution of the assignment problem

Abstract

This paper discusses efforts to develop parallel algorithms that can be used to solve large-scale assignment problems typical of military battle management systems. Attempts to parallellze the classical Hungarian method are explored. Drawing on experimental data, a regresslon model is derived that relates the Hungarian method's run time to a cubic function of the number of parallel processors used in the solution. Four parallel heuristics for solving the assignment problem are developed and analysed. Two of them perform well in a parallel environment. The first, based on Vagel's approximation, can be used to identify a feasible, near-optimal assignment. The second algorithm partitions the assignment problem into independent subproblems across the parallel array. The resulting solution, although infeasible in the strict definition of the assignment problem, is seen to be reasonably good and can be obtained very rapidly. Either of these two heuristics are of potential use in the stringent computing environment of a real-time resource management system.