Skip to main content
Book cover

Algorithms - ESA 2015 pp 619–630Cite as

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

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9294)

Abstract

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(mn 2) 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.

Keywords

  • 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.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-662-48350-3_52
  • Chapter length: 12 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   109.00
Price excludes VAT (USA)
  • ISBN: 978-3-662-48350-3
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   139.99
Price excludes VAT (USA)
Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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)

    CrossRef  Google Scholar 

  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)

    CrossRef  MATH  Google Scholar 

  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)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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. Cherkassky, B.V., Goldberg, A.V.: On Implementing Push-Relabel Method for the Maximum Flow Problem. Algorithmica 19, 390–410 (1997)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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. 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. 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)

    CrossRef  Google Scholar 

  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. Ford Jr., L.R., Fulkerson, D.R.: Maximal Flow Through a Network. Canadian Journal of Math. 8, 399–404 (1956)

    MathSciNet  CrossRef  MATH  Google Scholar 

  11. Gallo, G., Grigoriadis, M.D., Tarjan, R.E.: A Fast Parametric Maximum Flow Algorithm and Applications. SIAM J. Comput. 18, 30–55 (1989)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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. 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)

    CrossRef  Google Scholar 

  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)

    CrossRef  Google Scholar 

  15. Goldberg, A.V., Tarjan, R.E.: A New Approach to the Maximum Flow Problem. J. Assoc. Comput. Mach. 35, 921–940 (1988)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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)

    MathSciNet  CrossRef  Google Scholar 

  17. Hao, J., Orlin, J.B.: A Faster Algorithm for Finding the Minimum Cut in a Directed Graph. J. Algorithms 17, 424–446 (1994)

    MathSciNet  CrossRef  MATH  Google Scholar 

  18. Hochbaum, D.S.: The pseudoflow algorithm: A new algorithm for the maximum-flow problem. Operations Research 56(4), 992–1009 (2008)

    MathSciNet  CrossRef  MATH  Google Scholar 

  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)

    CrossRef  Google Scholar 

  20. Kohli, P., Torr, P.H.S.: Measuring uncertainty in graph cut solutions. Computer Vision and Image Understanding 112(1), 30–38 (2008)

    CrossRef  Google Scholar 

  21. Sýkora, D., Dingliana, J., Collins, S.: Lazybrush: Flexible painting tool for hand-drawn cartoons. Comput. Graph. Forum 28(2), 599–608 (2009)

    CrossRef  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Amazon.com Inc., Seattle, USA

    Andrew V. Goldberg & Renato F. Werneck

  2. School of Computer Science, Tel Aviv University, Tel Aviv, Israel

    Sagi Hed & Haim Kaplan

  3. Microsoft Research, Cambridge, UK

    Pushmeet Kohli

  4. Department of Computer Science, Princeton University and Intertrust Technologies, Princeton, USA

    Robert E. Tarjan

Authors
  1. Andrew V. Goldberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sagi Hed
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haim Kaplan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Pushmeet Kohli
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Robert E. Tarjan
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Renato F. Werneck
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrew V. Goldberg .

Editor information

Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Goldberg, A.V., Hed, S., Kaplan, H., Kohli, P., Tarjan, R.E., Werneck, R.F. (2015). Faster and More Dynamic Maximum Flow by Incremental Breadth-First Search. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_52

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-48350-3_52

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48349-7

  • Online ISBN: 978-3-662-48350-3

  • eBook Packages: Computer ScienceComputer Science (R0)