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Rapidly computing robust minimum capacity s-t cuts: a case study in solving a sequence of maximum flow problems

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  • Douglas Altner
  • Özlem Ergun

Abstract

The Minimum Capacity s-t Cut Problem (MinCut) is an intensively studied problem in combinatorial optimization. A natural extension is the problem of choosing a minimum capacity s-t cut when arc capacities are unknown but confined to known intervals. This motivates the Robust Minimum Capacity s-t Cut Problem (RobuCut), which has applications such as open-pit mining and project scheduling. In this paper, we show how RobuCut can be reduced to solving a sequence of maximum flow problems and provide an efficient algorithm for rapidly solving this sequence of problems. We demonstrate that our algorithm solves instances of RobuCut in seconds that would require hours if a standard maximum flow solver is iteratively used as a black-box subroutine. Copyright US Government 2011

Suggested Citation

  • Douglas Altner & Özlem Ergun, 2011. "Rapidly computing robust minimum capacity s-t cuts: a case study in solving a sequence of maximum flow problems," Annals of Operations Research, Springer, vol. 184(1), pages 3-26, April.
    • Handle: RePEc:spr:annopr:v:184:y:2011:i:1:p:3-26:10.1007/s10479-010-0730-1
    DOI: 10.1007/s10479-010-0730-1
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    1. Dawn M. Strickland & Earl Barnes & Joel S. Sokol, 2005. "Optimal Protein Structure Alignment Using Maximum Cliques," Operations Research, INFORMS, vol. 53(3), pages 389-402, June.
    2. Johannes O. Royset & R. Kevin Wood, 2007. "Solving the Bi-Objective Maximum-Flow Network-Interdiction Problem," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 175-184, May.
    3. Alper Atamtürk & Muhong Zhang, 2007. "Two-Stage Robust Network Flow and Design Under Demand Uncertainty," Operations Research, INFORMS, vol. 55(4), pages 662-673, August.
    4. A. Ben-Tal & A. Nemirovski, 1998. "Robust Convex Optimization," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 769-805, November.
    5. Rolf H. Möhring & Andreas S. Schulz & Frederik Stork & Marc Uetz, 2003. "Solving Project Scheduling Problems by Minimum Cut Computations," Management Science, INFORMS, vol. 49(3), pages 330-350, March.
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    Cited by:

    1. W. Lambert & A. Newman, 2014. "Tailored Lagrangian Relaxation for the open pit block sequencing problem," Annals of Operations Research, Springer, vol. 222(1), pages 419-438, November.

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