Rapidly solving an online sequence of maximum flow problems with extensions to computing robust minimum cuts

Abstract

We investigate how to rapidly solve an online sequence of maximum flow problems (MFPs). Such sequences arise in a diverse collection of settings including stochastic network programming and constraint programming. In this paper, we formalize the study of solving a sequence of MFPs, introduce a maximum flow algorithm designed for "warm starts" and extend our work to computing a robust minimum cut. We demonstrate that our algorithms reduce the running time by an order of magnitude when compared similar codes that use a black-box MFP solver. In particular, we show that our algorithm for robust minimum cuts can solve instances in seconds that would require over four hours using a black-box maximum flow solver. © 2008 Springer-Verlag Berlin Heidelberg.