A Graph-Theoretic Approach to a Class of Integer-Programming Problems

Abstract

This paper presents an efficient algorithm for finding a minimum-weight generalized matching in a weighted bipartite graph. Computational evidence is given that indicates that the time required to find a least-cost assignment of n jobs to n workers goes roughly as n² for 10 ≦ n ≦ 50. It is shown that this algorithm can be used to solve effectively the well known transportation problem of integer programming where the objective function is convex-separable. Finally, the paper gives an algorithm that applies the same concept to a graph that is not necessarily bipartite.