Article

Distributed algorithms for multicommodity flow problems via approximate steepest descent framework

Authors:

Baruch Awerbuch,

Rohit Khandekar,

Satish RaoAuthors Info & Claims

SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms

Pages 949 - 957

Published: 07 January 2007 Publication History

Get Access

Abstract

We consider solutions for distributed multicommodity flow problems, which are solved by multiple agents operating in a cooperative but uncoordinated manner. We show first distributed solutions that allow 1 + ε approximation and whose convergence time is essentially linear in the maximal path length, and is independent of the number of commodities and the size of the graph.

Our algorithms use a very natural approximate steepest descent framework, combined with a blocking flow technique to speed up the convergence in distributed and parallel environment.

Previously known solutions that achieved comparable convergence time and approximation ratio required exponential computational and space overhead per agent.

References

[1]

{AA94} B. Awerbuch and Y. Azar. Local optimization of global objectives: Competitive distributed deadlock resolution and resource allocation. In Proc. 35th IEEE Symp. on Found. of Comp. Science, pages 240--249, 1994.

Google Scholar

[2]

{ANR92} Y. Azar, J. Naor, and R. Rom. The competitiveness of on-line assignment. In Proc. 3rd ACM-SIAM Symp. on Discrete Algorithms, pages 203--210, 1992.

Digital Library

Google Scholar

[3]

{BBR97} Y. Bartal, J. W. Byers, and D. Raz. Global optimization using local information with applications to flow control. In Proc. 38th IEEE Symp. on Found. of Comp. Science, pages 303--312, 1997.

Digital Library

Google Scholar

[4]

{EDM05} E. Even-Dar and Y. Mansour. Fast convergence of selfish rerouting. In Proc. 16th ACM-SIAM Symp. on Discrete Algorithms, pages 772--781, 2005.

Digital Library

Google Scholar

[5]

{Fle00} L. K. Fleischer. Approximating fractional multicommodity flow independent of the number of commodities. SIAM Journal on Discrete Mathematics, 13:505--520, 2000.

Digital Library

Google Scholar

[6]

{FRV06} S. Fischer, H. Räcke, and B. Vöcking. Fast convergence to Wardrop equilibria by adaptive sampling methods. In Proc. 38th ACM Symp. on Theory of Computing, pages 653--662, 2006.

Digital Library

Google Scholar

[7]

{GK98} N. Garg and J. Könemann. Faster and simpler algorithms for multicommodity flow and other fractional packing problems. In Proc. 39th IEEE Symp. on Found. of Comp. Science, pages 300--309, 1998.

Digital Library

Google Scholar

[8]

{GY02} N. Garg and N. E. Young. On-line end-to-end congestion control. In Proc. 43rd IEEE Symp. on Found. of Comp. Science, pages 538--546, 2002.

Digital Library

Google Scholar

[9]

{LN93} M. Luby and N. Nissan. A parallel approximation algorithm for positive linear programming. In Proc. 25th ACM Symp. on Theory of Computing, pages 448--457, 1993.

Digital Library

Google Scholar

[10]

{PST95} S. Plotkin, D. Shmoys, and E. Tardos. Fast approximation algorithms for fractional packing and covering problems. Math of Oper. Research, 20:257--301, 1995.

Digital Library

Google Scholar

[11]

{You01} N. E. Young. Sequential and parallel algorithms for mixed packing and covering. In Proc. 42nd IEEE Symp. on Found. of Comp. Science, pages 538--546, 2001.

Digital Library

Google Scholar

Cited By

View all

Feng YLi BLi BBabaguchi NAizawa KSmith JSatoh SPlagemann THua XYan R(2012)JetwayProceedings of the 20th ACM international conference on Multimedia10.1145/2393347.2393388(259-268)Online publication date: 29-Oct-2012
https://dl.acm.org/doi/10.1145/2393347.2393388
Kleinberg RPiliouras GTardos É(2011)Load balancing without regret in the bulletin board modelDistributed Computing10.1007/s00446-011-0129-524:1(21-29)Online publication date: 1-Sep-2011
https://dl.acm.org/doi/10.1007/s00446-011-0129-5
Chu SWang X(2010)MIMO-aware routing in wireless mesh networksProceedings of the 29th conference on Information communications10.5555/1833515.1833872(2784-2792)Online publication date: 14-Mar-2010
https://dl.acm.org/doi/10.5555/1833515.1833872
Show More Cited By

Distributed algorithms for multicommodity flow problems via approximate steepest descent framework
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis

Recommendations

Distributed algorithms for multicommodity flow problems via approximate steepest descent framework

We consider solutions for distributed multicommodity flow problems, which are solved by multiple agents operating in a cooperative but uncoordinated manner. We show first distributed solutions that allow (1 + ϵ) approximation and whose convergence time ...
Fast Approximation Algorithms for Multicommodity Flow Problems

All previously known algorithms for solving the multicommodity flow problem with capacities are based on linear programming. The best of these algorithms uses a fast matrix multiplication algorithm and takes O(k3.5n3m0.5 log(nDU)) time for the ...
Fast approximation algorithms for multicommodity flow problems

Comments

Information & Contributors

Information

Published In

SODA '07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms

January 2007

1322 pages

ISBN:9780898716245

Conference Chair:
Harold Gabow
University of Colorado, Boulder

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 07 January 2007

Check for updates

Qualifiers

Article

Acceptance Rates

SODA '07 Paper Acceptance Rate 139 of 382 submissions, 36%;

Overall Acceptance Rate 411 of 1,322 submissions, 31%

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

11
Total Citations
View Citations
277
Total Downloads

Downloads (Last 12 months)1
Downloads (Last 6 weeks)1

Reflects downloads up to 30 Aug 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Feng YLi BLi BBabaguchi NAizawa KSmith JSatoh SPlagemann THua XYan R(2012)JetwayProceedings of the 20th ACM international conference on Multimedia10.1145/2393347.2393388(259-268)Online publication date: 29-Oct-2012
https://dl.acm.org/doi/10.1145/2393347.2393388
Kleinberg RPiliouras GTardos É(2011)Load balancing without regret in the bulletin board modelDistributed Computing10.1007/s00446-011-0129-524:1(21-29)Online publication date: 1-Sep-2011
https://dl.acm.org/doi/10.1007/s00446-011-0129-5
Chu SWang X(2010)MIMO-aware routing in wireless mesh networksProceedings of the 29th conference on Information communications10.5555/1833515.1833872(2784-2792)Online publication date: 14-Mar-2010
https://dl.acm.org/doi/10.5555/1833515.1833872
Kleinberg RPiliouras GTardos ÉTirthapura SAlvisi L(2009)Load balancing without regret in the bulletin board modelProceedings of the 28th ACM symposium on Principles of distributed computing10.1145/1582716.1582731(56-62)Online publication date: 10-Aug-2009
https://dl.acm.org/doi/10.1145/1582716.1582731
Awerbuch BKhandekar R(2009)Greedy distributed optimization of multi-commodity flowsDistributed Computing10.1007/s00446-008-0074-021:5(317-329)Online publication date: 1-Feb-2009
https://dl.acm.org/doi/10.1007/s00446-008-0074-0
Awerbuch BKhandekar R(2008)Stateless near optimal flow control with poly-logarithmic convergenceProceedings of the 8th Latin American conference on Theoretical informatics10.5555/1792918.1792968(580-592)Online publication date: 7-Apr-2008
https://dl.acm.org/doi/10.5555/1792918.1792968
Awerbuch BKhandekar RLadner RDwork C(2008)Stateless distributed gradient descent for positive linear programsProceedings of the fortieth annual ACM symposium on Theory of computing10.1145/1374376.1374476(691-700)Online publication date: 17-May-2008
https://dl.acm.org/doi/10.1145/1374376.1374476
Fischer SOlbrich LVöcking B(2008)Approximating Wardrop equilibria with finitely many agentsDistributed Computing10.1007/s00446-008-0057-121:2(129-139)Online publication date: 1-Jul-2008
https://dl.acm.org/doi/10.1007/s00446-008-0057-1
Awerbuch BKhandekar RGupta IWattenhofer R(2007)Minimizing the total cost of network measurements in a distributed mannerProceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing10.1145/1281100.1281170(354-355)Online publication date: 12-Aug-2007
https://dl.acm.org/doi/10.1145/1281100.1281170
Awerbuch BKhandekar RGupta IWattenhofer R(2007)Distributed network monitoring and multicommodity flowsProceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing10.1145/1281100.1281141(284-291)Online publication date: 12-Aug-2007
https://dl.acm.org/doi/10.1145/1281100.1281141
Show More Cited By

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.

Cited By

Recommendations

Distributed algorithms for multicommodity flow problems via approximate steepest descent framework

Fast Approximation Algorithms for Multicommodity Flow Problems

Fast approximation algorithms for multicommodity flow problems