Solving Minimum-Cost Flow Problems by Successive Approximation

Abstract:

We introduce a framework for solving minimum-cost flow problems. Our approach measures the quality of a solution by the amount that the complementary slackness conditions are violated. We show how to extend techniques developed for the maximum flow problem to improve the quality of a solution.
This framework allows us to achieve O(min(n3, n5/3m2/3, nm log n)log(nC)) running time.