Skip to main content
SpringerLink
Log in

A New Min-Cut Max-Flow Ratio for Multicommodity Flows

  • Conference paper
  • First Online:
Integer Programming and Combinatorial Optimization (IPCO 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2337))

Abstract

We present an improved bound on the min-cut max-flow ratio for multicommodity flow problems with specified demands. To obtain the numerator of this ratio, capacity of a cut is scaled by the demand that has to cross the cut. In the denominator, the maximum concurrent flow value is used. Our new bound is proportional to log(k*) where k* is the cardinality of the minimal vertex cover of the demand graph.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Y. Aumann and Y. Rabani: Approximate min-cut max-flow theorem and approximation algorithm. SIAM Journal on Computing 27 (1998) 291–301

    Article  MathSciNet  MATH  Google Scholar 

  2. D. Bienstock and O. Günlük: Computational experience with a difficult multicommodity flow problem. Mathematical Programming 68 (1995) 213–238

    MathSciNet  MATH  Google Scholar 

  3. J. Bourgain: On Lipschitz embedding of finite metric spaces in Hilbert space. Israel Journal of Mathematics 52 (1985) 46–52

    Article  MathSciNet  MATH  Google Scholar 

  4. ”P. Fishburn and P. Hammer: Bipartite dimensions and bipartite degrees of graphs. Discrete Math. 160 (1996) 127–148

    Article  MathSciNet  MATH  Google Scholar 

  5. L. R. Ford Jr. and D. R. Fulkerson: Flows in Networks. Princeton University Press (1962)

    Google Scholar 

  6. N. Garg, V.V. Vazirani and M. Yannakakis: Approximate max-flow min-(multi)cut theorems and their applications. in Proceedings of the 25th Annual ACM Symposium on Theory of Computing (1993) 698–707

    Google Scholar 

  7. M. Iri: On an extension of the max-flow min-cut theorem to multicommodity flows. Journal of the Operations Research Society of Japan 13 (1971) 129–135

    MathSciNet  MATH  Google Scholar 

  8. W. Johnson and J. Lindenstrauss: Extensions of Lipschitz mappings into a Hilbert space. Contemporary Mathematics 26 (1984) 189–206

    Article  MathSciNet  MATH  Google Scholar 

  9. A. V. Karzanov: Polyhedra related to undirected multicommodity flows. Linear Algebra and its Applications 114 (1989) 293–328

    Article  MathSciNet  Google Scholar 

  10. P. Klein, S. Rao, A. Agrawal, and R. Ravi: An approximate max-flow min-cut relation for undirected multicommodity flow with applications. Combinatorica 15 (1995) 187–202

    Article  MathSciNet  MATH  Google Scholar 

  11. F.T. Leighton and S. Rao: An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms. in Proceedings of the 29th Annual IEEE Symposium on Foundations of Computer Science (1988) 422–431

    Google Scholar 

  12. N. Linial, E. London, and Y. Rabinovich (1995): The geometry of graphs and some of its algorithmic applications. Combinatorica 15 215–245

    Article  MathSciNet  MATH  Google Scholar 

  13. C. Lund, S. Phillips and N. Reingold: Private communication

    Google Scholar 

  14. D. W. Matula: Concurrent flow and concurrent connectivity in graphs. in Graph Theory and its Applications to Algorithms and Computer Science Wiley New York (1985) 543–559

    Google Scholar 

  15. R. Motwani and P. Raghavan: Randomized Algorithms. Cambridge University Press Cambridge (1995)

    Book  MATH  Google Scholar 

  16. H. Okamura and P. Seymour: Multicommodity flows in planar graphs. Journal of Comput. Theory-Ser. B 31 (1981) 75–81

    Article  MathSciNet  MATH  Google Scholar 

  17. K. Onaga, and O. Kakusho: On feasibility conditions of multicommodity flows in networks. IEEE Transactions on Circuit Theory CT-18 4 (1971) 425–429

    Article  MathSciNet  Google Scholar 

  18. G. Pisier: The Volume of Convex Bodies and Banach Space Geometry. Cambridge University Press Cambridge (1989)

    Book  MATH  Google Scholar 

  19. S. Plotkin and E. Tardos: Improved Bounds on the max-flow min-cut ratio for multicommodity flows. Proceedings 25’th Symposium on Theory of Computing (1993)

    Google Scholar 

  20. F. Shahrokhi and D. W. Matula: The maximum concurrent flow problem. Journal of Association for Computing Machinery 37 (1990) 318–334

    Article  MathSciNet  MATH  Google Scholar 

  21. S. Tragoudas: Improved approximations for the min-cut max-flow ratio and the flux. Mathematical Systems Theory 29 (1996) 157–167

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Math. Sci. Dept., IBM Research, Yorktown Heights, NY, 10598

    Oktay Günlük

Authors
  1. Oktay Günlük
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Program in Applied and Computational Mathematics, University of Princeton, Fine Hall, Washington Road, Princeton, NJ, 08544-1000, USA

    William J. Cook

  2. Sloan School of Management, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139-4307, USA

    Andreas S. Schulz

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Günlük, O. (2002). A New Min-Cut Max-Flow Ratio for Multicommodity Flows. In: Cook, W.J., Schulz, A.S. (eds) Integer Programming and Combinatorial Optimization. IPCO 2002. Lecture Notes in Computer Science, vol 2337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47867-1_5

Download citation

  • DOI: https://doi.org/10.1007/3-540-47867-1_5

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43676-8

  • Online ISBN: 978-3-540-47867-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation