The assignment problem

Abstract

The linear assignment problem requires the determination of an optimal permutation vector for the assignment of tasks to agents. Even the backtracking implementation supports a rather powerful bounding function. Since the processing of permutation families (based on low-subscripted vector assignments) can be done independently of each other, one may examine parallel processing strategies, and discovery of instances in which the parallel execution is a very bad idea. Because of article size limitations, this article discusses only backtracking in parallel. A later article will address branch-and-bound in parallel.