Experimental Evaluation of Parametric Max-Flow Algorithms

  • Maxim Babenko
  • Jonathan Derryberry
  • Andrew Goldberg
  • Robert Tarjan
  • Yunhong Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4525)

Abstract

The parametric maximum flow problem is an extension of the classical maximum flow problem in which the capacities of certain arcs are not fixed but are functions of a single parameter. Gallo et al. [6] showed that certain versions of the push-relabel algorithm for ordinary maximum flow can be extended to the parametric problem while only increasing the worst-case time bound by a constant factor. Recently Zhang et al. [14,13] proposed a novel, simple balancing algorithm for the parametric problem on bipartite networks. They claimed good performance for their algorithm on networks arising from a real-world application. We describe the results of an experimental study comparing the performance of the balancing algorithm, the GGT algorithm, and a simplified version of the GGT algorithm, on networks related to those of the application of Zhang et al. as well as networks designed to be hard for the balancing algorithm. Our implementation of the balancing algorithm beats both versions of the GGT algorithm on networks related to the application, thus supporting the observations of Zhang et al. On the other hand, the GGT algorithm is more robust; it beats the balancing algorithm on some natural networks, and by asymptotically increasing amount on networks designed to be hard for the balancing algorithm.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahuja, R.K., Orlin, J.B., Stein, C., Tarjan, R.E.: Improved algorithms for bipartite network flow. SIAM Journal on Computing 23(5), 906–933 (1994)MATHCrossRefMathSciNetGoogle Scholar
  2. Babenko, M.A., Goldberg, A.V.: Experimental evaluation of a parametric flow algorithm. Technical report, Microsoft Research (2006)Google Scholar
  3. Balinski, M.L.: On a selection problem. Management Science 17(3), 230–231 (1970)MathSciNetMATHGoogle Scholar
  4. Cherkassky, B.V., Goldberg, A.V.: On Implementing Push-Relabel Method for the Maximum Flow Problem. Algorithmica 19, 390–410 (1997)MATHCrossRefMathSciNetGoogle Scholar
  5. Eisner, M.J., Severance, D.G.: Mathematical techniques for efficient record segmentation in large shared databases. J. ACM 23(4), 619–635 (1976)MATHCrossRefMathSciNetGoogle Scholar
  6. Gallo, G., Grigoriadis, M.D., Tarjan, R.E.: A fast parametric maximum flow algorithm and applications. SIAM J. Comput. 18(1), 30–55 (1989)MATHCrossRefMathSciNetGoogle Scholar
  7. Goldberg, A.V., Rao, S.: Beyond the flow decomposition barrier. J. ACM 45(5), 783–797 (1998)MATHCrossRefMathSciNetGoogle Scholar
  8. Goldberg, A.V., Tarjan, R.E.: A new approach to the maximum-flow problem. J. ACM 35(4), 921–940 (1988)MATHCrossRefMathSciNetGoogle Scholar
  9. Hochbaum, D.S.: The Pseudoflow Algorithm and the Pseudoflow-Based Simplex for the Maximum Flow Problem. In: Bixby, R.E., Boyd, E.A., Ríos-Mercado, R.Z. (eds.) Integer Programming and Combinatorial Optimization. LNCS, vol. 1412, pp. 325–337. Springer, Heidelberg (1998)Google Scholar
  10. King, V., Rao, S., Tarjan, R.: A Faster Deterministic Maximum Flow Algorithm. J. Algorithms 17, 447–474 (1994)CrossRefMathSciNetGoogle Scholar
  11. Mamer, J., Smith, S.: Optimizing field repair kits based on job completion rate. Management Science 28(11), 1328–1333 (1982)MATHGoogle Scholar
  12. Rhys, J.M.W.: A selection problem of shared fixed costs and network flows. Management Science 17(3), 200–207 (1970)CrossRefMATHGoogle Scholar
  13. Tarjan, R., Ward, J., Zhang, B., Zhou, Y., Mao, J.: Balancing applied to maximum network flow problems. In: Azar, Y., Erlebach, T. (eds.) ESA 2006. LNCS, vol. 4168, pp. 612–623. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  14. Zhang, B., Ward, J., Feng, Q.: Simultaneous parametric maximum flow algorithm with vertex balancing. Technical Report HPL-2005-121, HP Labs (2005)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Maxim Babenko
    • 1
  • Jonathan Derryberry
    • 2
  • Andrew Goldberg
    • 3
  • Robert Tarjan
    • 2
  • Yunhong Zhou
    • 2
  1. 1.Moscow State University, MoscowRussia
  2. 2.HP Labs, 1501 Page Mill Rd, Palo Alto, CA 94304 
  3. 3.Microsoft Research – SVC, 1065 La Avenida, Mountain View, CA 94043 

Personalised recommendations