A cycle augmentation algorithm for minimum cost multicommodity flows on a ring

Abstract

Minimum cost multicommodity flows are a useful model for bandwidth allocation problems. These problems are arising more frequently as regional service providers wish to carry their traffic over some national core network. We describe a simple and practical to find a minimum cost multicommodity flow in a ring network. Apart from 1 and 2-commodity flow problems, this seems to be the only such combinatorial augmentation algorithm for a version of exact mincost multicommodity flow. The solution it produces is always a half-integral, and by increasing the capacity of each link by one, we may also find an integral routing of no greater cost. The pivots in the are determined by choosing an /spl epsiv/>0, increasing and decreasing sets of variables, and adjusting these variables up or down accordingly by /spl epsiv/. In this sense, it generalizes the cycle cancelling algorithms for (single source) mincost flow. Although the is easily stated, proof of its correctness and polynomially bounded running time are more complex.