Rapidly Solving an Online Sequence of Maximum Flow Problems with Extensions to Computing Robust Minimum Cuts

  • Doug Altner
  • Özlem Ergun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5015)


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.


Maximum Flow Reoptimization Robust Minimum Cut 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bertsimas, D., Sim, M.: Robust Discrete Optimization and Network Flows. Mathematical Programming 98(1), 49–71 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Carr, R.: Separating Clique Trees and Bipartition Inequalities Having a Fixed Number of Handles and Teeth in Polynomial Time. Mathematics of Operations Research 22(2), 257–265 (1997)zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Cherkassky, B., Goldberg, A.: On Implementing Push-Relabel Method for the Maximum Flow Problem. Algorithmica 19(4), 390–410 (1994)CrossRefMathSciNetGoogle Scholar
  4. 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
  5. 5.
    Ford, L.R., Fulkerson, D.R.: Maximal Flow Through a Network. Canadian Journal of Mathematics 8, 399–404 (1956)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Goldberg, A.: Andrew Goldberg’s Network Optimization Library,
  7. 7.
    Goldberg, A., Tarjan, R.: A New Approach to the Maximum Flow Problem. Journal of Associated Computing Machinery 35 (1988)Google Scholar
  8. 8.
    Hochbaum, D., Chen, A.: Improved Planning for the Open - Pit Mining Problem. Operations Research 48, 894–914 (2000)CrossRefGoogle Scholar
  9. 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
  10. 10.
    Royset, J., Wood, R.K.: Solving the Bi-objective Maximum-Flow Network-Interdiction Problem. INFORMS Journal on Computing 19, 175–184 (2007)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Strickland, D., Barnes, E., Sokol, J.: Optimal Protein Structure Alignment Using Maximum Cliques. Operations Research (to appear, 2008)Google Scholar
  12. 12.
    Stone, H.S.: Multiprocessor Scheduling with the Aid of Network Flow Algorithms. IEEE Transactions on Software Engineering 3(1), 85–93 (1977)CrossRefGoogle Scholar
  13. 13.
    Wallace, S.: Investing in Arcs in a Network to Maximize the Expected Max Flow. Networks 17, 87–103 (1987)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Doug Altner
    • 1
  • Özlem Ergun
    • 1
  1. 1.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaGeorgia

Personalised recommendations