Two-Level Push-Relabel Algorithm for the Maximum Flow Problem

  • Andrew V. Goldberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5564)

Abstract

We describe a two-level push-relabel algorithm for the maximum flow problem and compare it to the competing codes. The algorithm generalizes a practical algorithm for bipartite flows. Experiments show that the algorithm performs well on several problem families.

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References

  1. 1.
    Ahuja, R.K., Orlin, J.B., Stein, C., Tarjan, R.E.: Improved algorithms for bipartite network flow problems. SIAM J. Comp. (to appear)Google Scholar
  2. 2.
    Babenko, M., Derryberry, J., Goldberg, A.V., Tarjan, R.E., Zhou, Y.: Experimental evaluation of parametric maximum flow algorihtms. In: Demetrescu, C. (ed.) WEA 2007. LNCS, vol. 4525, pp. 256–269. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  3. 3.
    Boykov, Y., Kolmogorov, V.: An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision. IEEE transactions on Pattern Analysis and Machine Intelligence 26(9), 1124–1137 (2004)CrossRefMATHGoogle Scholar
  4. 4.
    Chandran, B., Hochbaum, D.: A computational study of the pseudoflow and push-relabel algorithms for the maximum flow problem (submitted for publication) (2007)Google Scholar
  5. 5.
    Cheriyan, J., Maheshwari, S.N.: Analysis of Preflow Push Algorithms for Maximum Network Flow. SIAM J. Comput. 18, 1057–1086 (1989)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Cherkassky, B.V.: A Fast Algorithm for Computing Maximum Flow in a Network. In: Karzanov, A.V. (ed.) Collected Papers, Combinatorial Methods for Flow Problems, vol. 3, pp. 90–96. The Institute for Systems Studies, Moscow (1979); English translation appears in AMS Trans. 158, 23–30 (1994) (in Russian)Google Scholar
  7. 7.
    Cherkassky, B.V., Goldberg, A.V.: On Implementing Push-Relabel Method for the Maximum Flow Problem. Algorithmica 19, 390–410 (1997)CrossRefMATHMathSciNetGoogle Scholar
  8. 8.
    Cherkassky, B.V., Goldberg, A.V., Martin anbd, P., Setubal, J.C., Stolfi, J.: Augment or push? a computational study of bipartite matching and unit capacity flow algorithms. Technical Report 98-036R, NEC Research Institute, Inc. (1998)Google Scholar
  9. 9.
    Derigs, U., Meier, W.: Implementing Goldberg’s Max-Flow Algorithm — A Computational Investigation. ZOR — Methods and Models of Operations Research 33, 383–403 (1989)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Derigs, U., Meier, W.: An Evaluation of Algorithmic Refinements and Proper Data-Structures for the Preflow-Push Approach for Maximum Flow. In: ASI Series on Computer and System Sciences, vol. 8, pp. 209–223. NATO (1992)Google Scholar
  11. 11.
    Ford, L.R., Fulkerson, D.R.: Maximal Flow Through a Network. Canadian Journal of Math. 8, 399–404 (1956)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Gabow, H.N.: Scaling Algorithms for Network Problems. J. of Comp. and Sys. Sci. 31, 148–168 (1985)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Goldberg, A.V.: An Efficient Implementation of a Scaling Minimum-Cost Flow Algorithm. J. Algorithms 22, 1–29 (1997)CrossRefMathSciNetGoogle Scholar
  14. 14.
    Goldberg, A.V., Kennedy, R.: An Efficient Cost Scaling Algorithm for the Assignment Problem. Math. Prog. 71, 153–178 (1995)MATHMathSciNetGoogle Scholar
  15. 15.
    Goldberg, A.V., Rao, S.: Beyond the Flow Decomposition Barrier. J. Assoc. Comput. Mach. 45, 753–782 (1998)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Goldberg, A.V., Tarjan, R.E.: A New Approach to the Maximum Flow Problem. J. Assoc. Comput. Mach. 35, 921–940 (1988)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Goldberg, A.V.: Recent developments in maximum flow algorithms. In: Arnborg, S. (ed.) SWAT 1998. LNCS, vol. 1432, pp. 1–10. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  18. 18.
    Goldberg, A.V.: The Partial Augment–Relabel Algorithm for the Maximum Flow Problem. In: Halperin, D., Mehlhorn, K. (eds.) Esa 2008. LNCS, vol. 5193, pp. 466–477. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Goldfarb, D., Grigoriadis, M.D.: A Computational Comparison of the Dinic and Network Simplex Methods for Maximum Flow. Annals of Oper. Res. 13, 83–123 (1988)CrossRefMathSciNetGoogle Scholar
  20. 20.
    Johnson, D.S., McGeoch, C.C.: Network Flows and Matching: First DIMACS Implementation Challenge. In: AMS, Proceedings of the 1-st DIMACS Implementation Challenge (1993)Google Scholar
  21. 21.
    King, V., Rao, S., Tarjan, R.: A Faster Deterministic Maximum Flow Algorithm. J. Algorithms 17, 447–474 (1994)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Mazzoni, G., Pallottino, S., Scutella, M.G.: The Maximum Flow Problem: A Max-Preflow Approach. Eur. J. of Oper. Res. 53, 257–278 (1991)CrossRefMATHGoogle Scholar
  23. 23.
    Negrus, C.S., Pas, M.B., Stanley, B., Stein, C., Strat, C.G.: Solving maximum flow problems on real world bipartite graphs. In: Proc. 11th International Workshop on Algorithm Engineering and Experiments, pp. 14–28. SIAM, Philadelphia (2009)Google Scholar
  24. 24.
    Iossa, A., Cerulli, R., Gentili, M.: Efficient Preflow Push Algorithms. Computers & Oper. Res. 35, 2694–2708 (2008)CrossRefMATHMathSciNetGoogle Scholar
  25. 25.
    Sleator, D.D., Tarjan, R.E.: A Data Structure for Dynamic Trees. J. Comput. System Sci. 26, 362–391 (1983)CrossRefMATHMathSciNetGoogle Scholar
  26. 26.
    Tuncel, L.: On the Complexity of Preflow-Push Algorithms for Maximum-Flow Problems. Algorithmica 11, 353–359 (1994)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Andrew V. Goldberg
    • 1
  1. 1.Microsoft Research – Silicon ValleyUSA

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