Article

Greedy distributed optimization of multi-commodity flows

Authors:

Baruch Awerbuch,

Rohit KhandekarAuthors Info & Claims

PODC '07: Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing

Pages 274 - 283

https://doi.org/10.1145/1281100.1281140

Published: 12 August 2007 Publication History

Abstract

The multi-commodity flow problem is a classical combinatorial optimization problem that addresses a number of practically important issues of congestion and bandwidth management in connection-oriented network architectures.

We consider solutions for distributed multi-commodity flow problems, which are solved by multiple agents operating in a cooperative but uncoordinated manner. We provide the first stateless greedy distributed algorithm for the concurrent multi-commodity flow problem with poly-logarithmic convergence. More precisely, our algorithm achieves (1+ε) approximation, with running time O(logP•log^O(1)m•(1/ε)^O(1) where P is the number of flow-paths in the network. No prior results exist for our model.

Our algorithm is a reasonable alternative to existing polynomial sequential approximation algorithms, such as Garg-Könemann [17]. The algorithm is simple and can be easily implemented or taught in a classroom.

Remarkably, our algorithm requires that the increase in the flow rate on a link is more aggressive than the decrease in the rate. Essentially all of the existing flow-control heuristics are variations of TCP, which uses a conservative cap on the increase (e.g., additive), and a rather liberal cap on the decrease (e.g., multiplicative). In contrast, our algorithm requires the increase to be multiplicative, and that this increase is dramatically more aggressive than the decrease.

References

[1]

B. Awerbuch and Y. Azar. Local optimization of global objectives: Competitive distributed deadlock resolution and resource allocation. FOCS, 1994.

Digital Library

[2]

B. Awerbuch, Y. Azar, and A. Epstein. The price of routing unsplittable flow. STOC, 2005.

Digital Library

[3]

B. Awerbuch, Y. Azar, Y. Richter, and D. Tsur. Tradeoffs in worst-case equilibria. WAOA, 2004.

[4]

B. Awerbuch and R. Khandekar. Distributed network monitoring and multicommodity flows: a primal-dual approach. PODC, 2007.

Digital Library

[5]

B. Awerbuch, R. Khandekar, and S. Rao. Distributed algorithms for multicommodity flow problems via approximate steepest descent framework. SODA, 2007.

Digital Library

[6]

B. Awerbuch and T. Leighton. A simple local-control approximation algorithm for multicommodity flow. FOCS, 1993.

Digital Library

[7]

B. Awerbuch and T. Leighton. Improved approximation algorithms for the multicommodity flow problem and local competitive routing in dynamic networks. STOC, 1994.

Digital Library

[8]

B. Awerbuch, B. Patt-Shamir, and G. Varghese. Self-stabilization by local checking and correction. FOCS, 1991.

Digital Library

[9]

B. Awerbuch and G. Varghese. Distributed program checking: a paradigm for building self-stabilizing distributed protocols. FOCS, 1991.

Digital Library

[10]

Y. Bartal, J. W. Byers, and D. Raz. Global optimization using local information with applications to flow control. FOCS, 1997.

Digital Library

[11]

S. Chien and A. Sinclair. Convergence to approximate nash equilibria in congestion games. SODA, 2007.

Digital Library

[12]

E. Dijkstra. Self stabilizing systems in spite of distributed control. CACM, 17:643--644, Nov 1974.

Digital Library

[13]

S. Dolev, A. Israeli, and S. Moran. Self-stabilization of dynamic systems assuming only read/write atomicity. PODC, 1990.

Digital Library

[14]

E. Even-Dar and Y. Mansour. Fast convergence of selfish rerouting. SODA, 2005.

Digital Library

[15]

S. Fischer, H. Racke, and B. Vocking. Fast convergence to wardrop equilibria by adaptive sampling methods. STOC, 2006.

Digital Library

[16]

S. Fischer and B. Vocking. Adaptive routing with stale information. PODC, 2005.

Digital Library

[17]

N. Garg and J. Könemann. Faster and simpler algorithms for multicommodity flow and other fractional packing problems. FOCS, 1998.

Digital Library

[18]

N. Garg and N. E. Young. On-line end-to-end congestion control. FOCS, 2002.

Digital Library

[19]

M. G. Gouda and N. J. Multari. Stabilizing communication protocols. Technical Report TR-90-20, Dept. of Computer Science, University of Texas at Austin, June 1990.

Digital Library

[20]

R. M. Karp, E. Koutsoupias, C. H. Papadimitriou, and S. Shenker. Optimization problems in congestion control. FOCS, 2000.

Digital Library

[21]

A. Khanna and J. A. Zinky. The revised arpanet routing metric. SIGCOMM, 1998.

Digital Library

[22]

P. Klein, S. Plotkin, C. Stein, and E. Tardos. Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts. STOC, 1990.

Digital Library

[23]

P. Klein, S. Plotkin, C. Stein, and E. Tardos. Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts. SIAM Journal on Computing, 1993.

Digital Library

[24]

E. Koutsoupias and C. Papadimitriou. Worst-case equilibria. Lecture Notes in Computer Science, 1563:404--413, 1999.

Digital Library

[25]

J. F. Kurose and K. W. Ross. Computer Networking, a top down approach featuring the Internet, 3rd ed. Addison-Wesley Longman, 2004.

Digital Library

[26]

C. Labovitz, A. Ahuja, and F. Jahanian. Experimental study of internet stability and wide-area backbone failures. Technical Report CSE-TR-382-98, University of Michigan, 1998.

[27]

T. Leighton, F. Makedon, S. Plotkin, C. Stein, E. Tardos, and S. Tragoudas. Fast approximation algorithms for multicommodity flow problem. STOC, 1991.

Digital Library

[28]

M. Luby and N. Nissan. A parallel approximation algorithm for positive linear programming. STOC, 1993.

Digital Library

[29]

J. McQuillan, I. Richer, and E. Rosen. The new routing algorithm for the arpanet. IEEE Trans. on Commun., 28(5):711--719, May 1980.

[30]

J. M. McQuillan, G. Falk, and I. Richer. A review of the development and performance of the arpanet routing algorithm. IEEE Trans. on Commun., 26(12):1802--1811, Dec. 1978.

[31]

V. Mirrokni, M. Goemans, and A. Vetta. Sink equilibria and convergence. FOCS, 2005.

Digital Library

[32]

S. Plotkin, D. Shmoys, and E. Tardos. Fast approximation algorithms for fractional packing and covering problems. Math of Oper. Research, pages 257--301, 1994.

Digital Library

[33]

J. Rexford. Handbook of Optimization in Telecommunications, Chapter on Route optimization in IP networks. Kluwer Academic Publishers, 2005.

[34]

T. Roughgarden. Selfish Routing. PhD thesis, Cornell University, Department of Computer Science, 2002.

Digital Library

[35]

N. E. Young. Sequential and parallel algorithms for mixed packing and covering. FOCS, 2001.

Digital Library

Cited By

Hussak WTrehan A(2023)Termination of amnesiac floodingDistributed Computing10.1007/s00446-023-00448-y36:2(193-207)Online publication date: 1-May-2023
https://doi.org/10.1007/s00446-023-00448-y
Jose LIbanez SAlizadeh MMcKeown N(2019)A Distributed Algorithm to Calculate Max-Min Fair Rates Without Per-Flow StateProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/3341617.33261353:2(1-42)Online publication date: 19-Jun-2019
https://dl.acm.org/doi/10.1145/3341617.3326135
Pickering MÉrdi GPeyton Jones SEisenberg R(2016)Pattern synonymsACM SIGPLAN Notices10.1145/3241625.297601351:12(80-91)Online publication date: 8-Sep-2016
https://dl.acm.org/doi/10.1145/3241625.2976013
Show More Cited By

Index Terms

Greedy distributed optimization of multi-commodity flows
1. Theory of computation
  1. Design and analysis of algorithms

Recommendations

Distributed network monitoring and multicommodity flows: a primal-dual approach
PODC '07: Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
A canonical distributed optimization problem is solving a Covering/Packing Linear Program in a distributed environment with fast convergence and low communication and space overheads. In this paper, we consider the following covering and packing ...
Greedy distributed optimization of unsplittable multicommodity flows
PODC '08: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing

We consider solutions for distributed unsplittable multicommodity flow problems, which are solved by multiple agents operating in a cooperative but uncoordinated manner. A requirement here is that each commodity routes its entire demand along a single ...
Greedy distributed optimization of multi-commodity flows

The multi-commodity flow problem is a classical combinatorial optimization problem that addresses a number of practically important issues of congestion and bandwidth management in connection-oriented network architectures. We consider solutions for ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

PODC '07: Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing

August 2007

424 pages

ISBN:9781595936165

DOI:10.1145/1281100

General Chair:
Indranil Gupta
UIUC, USA
,
Program Chair:
Rogert Wattenhofer
ETH Zurich, Switzerland

Copyright © 2007 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 12 August 2007

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Article

Conference

PODC07

Sponsor:

PODC07: ACM Symposium on Principles of Distributed Computing 2007

August 12 - 15, 2007

Oregon, Portland, USA

Acceptance Rates

Overall Acceptance Rate 740 of 2,477 submissions, 30%

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

29
Total Citations
View Citations
452
Total Downloads

Downloads (Last 12 months)16
Downloads (Last 6 weeks)2

Reflects downloads up to 27 Jul 2024

Other Metrics

View Author Metrics

Citations

Cited By

Hussak WTrehan A(2023)Termination of amnesiac floodingDistributed Computing10.1007/s00446-023-00448-y36:2(193-207)Online publication date: 1-May-2023
https://doi.org/10.1007/s00446-023-00448-y
Jose LIbanez SAlizadeh MMcKeown N(2019)A Distributed Algorithm to Calculate Max-Min Fair Rates Without Per-Flow StateProceedings of the ACM on Measurement and Analysis of Computing Systems10.1145/3341617.33261353:2(1-42)Online publication date: 19-Jun-2019
https://dl.acm.org/doi/10.1145/3341617.3326135
Pickering MÉrdi GPeyton Jones SEisenberg R(2016)Pattern synonymsACM SIGPLAN Notices10.1145/3241625.297601351:12(80-91)Online publication date: 8-Sep-2016
https://dl.acm.org/doi/10.1145/3241625.2976013
Marlow SPeyton Jones SKmett EMokhov A(2016)Desugaring Haskell's do-notation into applicative operationsACM SIGPLAN Notices10.1145/3241625.297600751:12(92-104)Online publication date: 8-Sep-2016
https://dl.acm.org/doi/10.1145/3241625.2976007
Tostes AMaia GDuarte-Figueiredo FLoureiro A(2015)Suggestion of routes for vehicles in vehicular networks using the multicommodity flow modelProceedings of the 2015 IEEE Symposium on Computers and Communication (ISCC)10.1109/ISCC.2015.7405556(451-456)Online publication date: 6-Jul-2015
https://dl.acm.org/doi/10.1109/ISCC.2015.7405556
Kandula SMenache ISchwartz RBabbula S(2014)Calendaring for wide area networksACM SIGCOMM Computer Communication Review10.1145/2740070.262633644:4(515-526)Online publication date: 17-Aug-2014
https://dl.acm.org/doi/10.1145/2740070.2626336
Liu HKandula SMahajan RZhang MGelernter D(2014)Traffic engineering with forward fault correctionACM SIGCOMM Computer Communication Review10.1145/2740070.262631444:4(527-538)Online publication date: 17-Aug-2014
https://dl.acm.org/doi/10.1145/2740070.2626314
Jin XLiu HGandhi RKandula SMahajan RZhang MRexford JWattenhofer R(2014)Dynamic scheduling of network updatesACM SIGCOMM Computer Communication Review10.1145/2740070.262630744:4(539-550)Online publication date: 17-Aug-2014
https://dl.acm.org/doi/10.1145/2740070.2626307
Gupta AVanbever LShahbaz MDonovan SSchlinker BFeamster NRexford JShenker SClark RKatz-Bassett E(2014)SDXACM SIGCOMM Computer Communication Review10.1145/2740070.262630044:4(551-562)Online publication date: 17-Aug-2014
https://dl.acm.org/doi/10.1145/2740070.2626300
Hoare T(2014)Laws of concurrent programmingACM SIGPLAN Notices10.1145/2666356.260400249:6(168-168)Online publication date: 9-Jun-2014
https://dl.acm.org/doi/10.1145/2666356.2604002
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.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents