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 &Ogr;(min(n3, n5/3 m2/3, nm log n) log (nC)) running time.