Faster Scaling Algorithms for Network Problems

摘要

This paper presents algorithms for the assignment problem, the transportation problem and the minimum cost flow problem of operations research. The algorithms finds a minimum cost solution, but run in time close to the best -known bounds for the corresponding problems without costs. For example, the assignment problem (equivalently, minimum cost matching on a bipartite graph) can be solved in O((sq rt n)nm log (nN)) time, where n, m and N denote the number of vertices, number of edges and largest magnitude of a cost; costs are assumed to be integral. The algorithms work by scaling. In each scales problem an approximate optimum solution is found, rather than an exact optimum.