article

On the max-flow min-cut ratio for directed multicommodity flows

Authors:

M. T. Hajiaghayi,

Tom LeightonAuthors Info & Claims

Theoretical Computer Science, Volume 352, Issue 1

Pages 318 - 321

https://doi.org/10.1016/j.tcs.2005.10.037

Published: 07 March 2006 Publication History

Abstract

We present a pure combinatorial problem whose solution determines max-flow min-cut ratio for directed multicommodity flows. In addition, this combinatorial problem has applications in improving the approximation factor of the greedy algorithm for the maximum edge disjoint path problem. More precisely, our upper bound improves the approximation factor for this problem to O(n^3/4).

References

[1]

[1] C. Chekuri, S. Khanna, Edge disjoint paths revisited, in: Proc. Fourteenth Annu. ACM-SIAM Symp. Discrete Algorithms, 2003, pp. 628-637.

Digital Library

Google Scholar

[2]

[2] J. Cheriyan, H.J. Karloff, Y. Rabani, Approximating directed multicuts, in: Proc. 42th Annu. Symp. Foundations of Computer Science, 2001, pp. 348-356.

Digital Library

Google Scholar

[3]

[3] A. Gupta, Improved results for directed multicut, in: Proc. Fourteenth Annu. ACM-SIAM Symp. Discrete Algorithms, 2003, pp. 454-455.

Digital Library

Google Scholar

[4]

[4] V. Guruswami, S. Khanna, R. Rajaraman, B. Shepherd, M. Yannakakis, Near-optimal hardness results and approximation algorithms for edge-disjoint paths and related problems, J. Comput. System Sci. 67 (2003) 473-496.

Digital Library

Google Scholar

[5]

[5] T. Leighton, S. Rao, Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms, J. ACM 46 (1999) 787-832.

Digital Library

Google Scholar

[6]

[6] M. Saks, A. Samorodnitsky, L. Zosin, A lower bound on the integrality gap for minimum multicut in directed networks, Combinatorica 24 (3) (2004) 525-530.

Digital Library

Google Scholar

[7]

[7] D.B. Shmoys, Cut problems and their application to divide-and-conquer, in: Approximation Algorithms for NP-hard Problem, PWS Publishing Company, 1997, pp. 192-235.

Digital Library

Google Scholar

[8]

[8] K. Varadarajan, G. Venkataraman, Graph decomposition and a greedy algorithm for edge-disjoint paths, in: Proc. Fifteenth Annu. ACM-SIAM Symp. Discrete Algorithms, 2004, pp. 379-380.

Digital Library

Google Scholar

Cited By

View all

Bouziane MGire SMonin FNana LChbeir RAgrawal RBiskri I(2016)Formal proof of security algorithms based on reachability reductionProceedings of the 8th International Conference on Management of Digital EcoSystems10.1145/3012071.3012085(67-72)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1145/3012071.3012085
Bauguion PBen-Ameur WGourdin E(2015)Efficient algorithms for the maximum concurrent flow problemNetworks10.1002/net.2157265:1(56-67)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1002/net.21572
Terruggia RBobbio A(2010)QoS analysis of weighted multi-state probabilistic networks via decision diagramsProceedings of the 29th international conference on Computer safety, reliability, and security10.5555/1886301.1886306(41-54)Online publication date: 14-Sep-2010
https://dl.acm.org/doi/10.5555/1886301.1886306
Show More Cited By

Index Terms

On the max-flow min-cut ratio for directed multicommodity flows
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
      1. Graph algorithms
  2. Mathematical analysis
    1. Functional analysis
      1. Approximation
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

Recommendations

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

In this paper we present a new bound on the min-cut max-flow ratio for multicommodity flow problems with specified demands. For multicommodity flows, this is a generalization of the well-known relationship between the capacity of a minimum cut and the ...
Bounds on the Max-Flow Min-Cut Ratio for Directed Multicommodity Flows
A tight max-flow min-cut duality theorem for nonlinear multicommodity flows
Abstract
The Max-Flow Min-Cut theorem is the classical duality result for the Max-Flow problem, which considers flow of a single commodity. We study a multiple commodity generalization of Max-Flow in which flows are composed of real-valued k-vectors ... $^{}$ $^{}$ $^{}$

Comments

Information & Contributors

Information

Published In

cover image Theoretical Computer Science

Theoretical Computer Science Volume 352, Issue 1

7 March 2006

348 pages

ISSN:0304-3975

Issue’s Table of Contents

Publisher

Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 07 March 2006

Author Tags

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

4
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 10 Nov 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Bouziane MGire SMonin FNana LChbeir RAgrawal RBiskri I(2016)Formal proof of security algorithms based on reachability reductionProceedings of the 8th International Conference on Management of Digital EcoSystems10.1145/3012071.3012085(67-72)Online publication date: 1-Nov-2016
https://dl.acm.org/doi/10.1145/3012071.3012085
Bauguion PBen-Ameur WGourdin E(2015)Efficient algorithms for the maximum concurrent flow problemNetworks10.1002/net.2157265:1(56-67)Online publication date: 1-Jan-2015
https://dl.acm.org/doi/10.1002/net.21572
Terruggia RBobbio A(2010)QoS analysis of weighted multi-state probabilistic networks via decision diagramsProceedings of the 29th international conference on Computer safety, reliability, and security10.5555/1886301.1886306(41-54)Online publication date: 14-Sep-2010
https://dl.acm.org/doi/10.5555/1886301.1886306
Krivelevich MNutov ZSalavatipour MVerstraete JYuster R(2007)Approximation algorithms and hardness results for cycle packing problemsACM Transactions on Algorithms10.1145/1290672.12906853:4(48-es)Online publication date: 1-Nov-2007
https://dl.acm.org/doi/10.1145/1290672.1290685

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Index Terms

Recommendations

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

Bounds on the Max-Flow Min-Cut Ratio for Directed Multicommodity Flows

A tight max-flow min-cut duality theorem for nonlinear multicommodity flows

Comments

Information

Published In

Publisher

Publication History

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations