Faster and More Dynamic Maximum Flow by Incremental Breadth-First Search

  • Andrew V. Goldberg
  • Sagi Hed
  • Haim Kaplan
  • Pushmeet Kohli
  • Robert E. Tarjan
  • Renato F. Werneck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)


We introduce the Excesses Incremental Breadth-First Search (Excesses IBFS) algorithm for maximum flow problems. We show that Excesses IBFS has the best overall practical performance on real-world instances, while maintaining the same polynomial running time guarantee of O(mn2) as IBFS, which it generalizes. Some applications, such as video object segmentation, require solving a series of maximum flow problems, each only slightly different than the previous. Excesses IBFS naturally extends to this dynamic setting and is competitive in practice with other dynamic methods.


Adjacency List Video Segmentation Free Vertex Distance Label Forward Phase 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alahari, K., Kohli, P., Torr, P.H.S.: Dynamic hybrid algorithms for MAP inference in discrete mrfs. IEEE PAMI 32(10), 1846–1857 (2010)CrossRefGoogle Scholar
  2. 2.
    Boykov, Y., Kolmogorov, V.: An Experimental Comparison of Min-Cut/Max-Flow Algorithms for Energy Minimization in Vision. IEEE PAMI 26(9), 1124–1137 (2004)CrossRefzbMATHGoogle Scholar
  3. 3.
    Chandran, B., Hochbaum, D.: A computational Study of the Pseudoflow and Push-Relabel Algorithms for the Maximum flow Problem. Operations Research 57, 358–376 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cherkassky, B.V.: A Fast Algorithm for Computing Maximum Flow in a Network. In: Karzanov, A.V. (ed.) Collected Papers, Vol. 3: Combinatorial Methods for Flow Problems, pp. 90–96. The Institute for Systems Studies, Moscow (1979) (in Russian) English translation appears in AMS Trans., 158, 23–30 (1994)Google Scholar
  5. 5.
    Cherkassky, B.V., Goldberg, A.V.: On Implementing Push-Relabel Method for the Maximum Flow Problem. Algorithmica 19, 390–410 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Delling, D., Goldberg, A.V., Razenshteyn, I., Werneck, R.F.: Graph partitioning with natural cuts. In: 25th IEEE IPDPS, pp. 1135–1146 (2011)Google Scholar
  7. 7.
    Delling, D., Goldberg, A.V., Razenshteyn, I., Werneck, R.F.: Exact combinatorial branch-and-bound for graph bisection. In: ALENEX, pp. 30–44 (2012)Google Scholar
  8. 8.
    Delling, D., Werneck, R.F.: Better bounds for graph bisection. In: Epstein, L., Ferragina, P. (eds.) ESA 2012. LNCS, vol. 7501, pp. 407–418. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  9. 9.
    Fishbain, B., Hochbaum, D.S., Mueller, S.: Competitive analysis of minimum-cut maximum flow algorithms in vision problems. CoRR, abs/1007.4531 (2010)Google Scholar
  10. 10.
    Ford Jr., L.R., Fulkerson, D.R.: Maximal Flow Through a Network. Canadian Journal of Math. 8, 399–404 (1956)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Gallo, G., Grigoriadis, M.D., Tarjan, R.E.: A Fast Parametric Maximum Flow Algorithm and Applications. SIAM J. Comput. 18, 30–55 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Goldberg, A.: Two Level Push-Relabel Algorithm for the Maximum Flow Problem. In: Proc. 5th Alg. Aspects in Info. Management. Springer, New York (2009)Google Scholar
  13. 13.
    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
  14. 14.
    Goldberg, A.V., Hed, S., Kaplan, H., Tarjan, R.E., Werneck, R.F.: Maximum flows by incremental breadth-first search. In: Demetrescu, C., Halldórsson, M.M. (eds.) ESA 2011. LNCS, vol. 6942, pp. 457–468. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    Goldberg, A.V., Tarjan, R.E.: A New Approach to the Maximum Flow Problem. J. Assoc. Comput. Mach. 35, 921–940 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Goldfarb, D., Grigoriadis, M.: A Computational Comparison of the Dinic and Network Simplex Methods for Maximum Flow. Ann. Op. Res. 13, 83–123 (1988)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Hao, J., Orlin, J.B.: A Faster Algorithm for Finding the Minimum Cut in a Directed Graph. J. Algorithms 17, 424–446 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Hochbaum, D.S.: The pseudoflow algorithm: A new algorithm for the maximum-flow problem. Operations Research 56(4), 992–1009 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Kohli, P., Torr, P.H.S.: Dynamic graph cuts for efficient inference in markov random fields. IEEE Trans. Pattern Anal. Mach. Intell. 29(12), 2079–2088 (2007)CrossRefGoogle Scholar
  20. 20.
    Kohli, P., Torr, P.H.S.: Measuring uncertainty in graph cut solutions. Computer Vision and Image Understanding 112(1), 30–38 (2008)CrossRefGoogle Scholar
  21. 21.
    Sýkora, D., Dingliana, J., Collins, S.: Lazybrush: Flexible painting tool for hand-drawn cartoons. Comput. Graph. Forum 28(2), 599–608 (2009)CrossRefGoogle Scholar
  22. 22.
    Verma, T., Batra, D.: Maxflow revisited: An empirical comparison of maxflow algorithms for dense vision problems. In: BMVC, pp. 1–12 (2012)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Andrew V. Goldberg
    • 1
  • Sagi Hed
    • 2
  • Haim Kaplan
    • 2
  • Pushmeet Kohli
    • 3
  • Robert E. Tarjan
    • 4
  • Renato F. Werneck
    • 1
  1. Inc.SeattleUSA
  2. 2.School of Computer ScienceTel Aviv UniversityTel AvivIsrael
  3. 3.Microsoft ResearchCambridgeUK
  4. 4.Department of Computer SciencePrinceton University and Intertrust TechnologiesPrincetonUSA

Personalised recommendations