Rapidly Solving an Online Sequence of Maximum Flow Problems with Extensions to Computing Robust Minimum Cuts
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.
KeywordsMaximum Flow Reoptimization Robust Minimum Cut
Unable to display preview. Download preview PDF.
- 4.Devanur, N., Papadimitriou, C., Saberi, A., Vazirani, V.: Market Equilibrium via a Primal-Dual Algorithm for a Convex Program. In: Proceedings of the 43rd Annual Symposium on Foundations of Computer Science (2002)Google Scholar
- 6.Goldberg, A.: Andrew Goldberg’s Network Optimization Library, http://avglab.com/andrew/soft.html
- 7.Goldberg, A., Tarjan, R.: A New Approach to the Maximum Flow Problem. Journal of Associated Computing Machinery 35 (1988)Google Scholar
- 9.Régin, J.C.: A Filtering Algorithm for Constraints of Difference in Constraint Satisfaction Problems. In: The Proceedings of the Twelfth National Conference on Artificial Intelligence, vol. 1, pp. 362–367 (1994)Google Scholar
- 11.Strickland, D., Barnes, E., Sokol, J.: Optimal Protein Structure Alignment Using Maximum Cliques. Operations Research (to appear, 2008)Google Scholar