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

Authors:
Doug Altner;Özlem Ergun
Affiliations:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia;H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia
Venue:
CPAIOR'08 Proceedings of the 5th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
Year:
2008

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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.