Faster Scaling Algorithms for Network Problems

This paper presents algorithms for the assignment problem, the transportation problem and the minimum cost flow problem of operations research. The algorithms find a minimum cost solution, but rtm 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(,/Vim 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. As in the work of Goldberg and Tazja [Go, GoT87a-b],in each scaled problem an approximate optimum solution is found, rather than an exact optimum.