Article

Stateless near optimal flow control with poly-logarithmic convergence

Authors:

Baruch Awerbuch,

Rohit KhandekarAuthors Info & Claims

LATIN'08: Proceedings of the 8th Latin American conference on Theoretical informatics

Pages 580 - 592

Published: 07 April 2008 Publication History

Abstract

We design completely local, stateless, and self-stabilizing flow control mechanism to be executed by "greedy" agents associated with individual flow paths. Our mechanism is very natural and can be described in a single line: If a path has many "congested" edges, decrease the flow on the path by a small multiplicative factor, otherwise increase its flow by a small multiplicative factor.

The mechanism does not require any initialization or coordination between the agents. We show that starting from an arbitrary feasible flow, the mechanism always maintains feasibility and reaches, after poly-logarithmic number of rounds, a 1+Ɛ approximation of the maximum throughput multicommodity flow. Moreover, the total number of rounds in which the solution is not 1+Ɛ approximate is also poly-logarithmic. Previous distributed solutions in our model either required a state since they used a primal-dual approach or had very slow (polynomial) convergence.

References

[1]

Awerbuch, B., Azar, Y., Khandekar, R.: Fast load balancing via bounded best response. In: SODA (2008).

Digital Library

[2]

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

Digital Library

[3]

Awerbuch, B., Khandekar, R.: Greedy distributed optimization of multi-commodity flows. In: PODC (2007).

Digital Library

[4]

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

Digital Library

[5]

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

Digital Library

[6]

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

Digital Library

[7]

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

Digital Library

[8]

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

Digital Library

[9]

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

Digital Library

[10]

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

Digital Library

[11]

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

Digital Library

[12]

Garg, N., Young, N.E.: On-line, end-to-end congestion control. In: FOCS (2002).

Digital Library

[13]

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

Digital Library

[14]

Koufogiannakis, C., Young, N.E.: Beating simplex for fractional packing and covering linear programs. In: FOCS (2007).

Digital Library

[15]

Kuhn, F.: The price of locality: exploring the complexity of distributed coordination primitives. PhD Thesis, ETH Zurich, Diss. ETH No. 16213, (December 2005).

[16]

Luby, M., Nisan, N.: A parallel approximation algorithm for positive linear programming. In: STOC (1993).

Digital Library

[17]

Plotkin, S., Shmoys, D., Tardos, E.: Fast approximation algorithms for fractional packing and covering problems. Math of Oper. Research 20(2), 257-301 (1994).

Digital Library

[18]

Young, N.E.: Sequential and parallel algorithms for mixed packing and covering. In: FOCS (2001).

Digital Library

Cited By

Allen-Zhu ZOrecchia LIndyk P(2015)Using optimization to break the epsilon barrierProceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms10.5555/2722129.2722224(1439-1456)Online publication date: 4-Jan-2015
https://dl.acm.org/doi/10.5555/2722129.2722224
Awerbuch BKhandekar RBazzi RPatt-Shamir B(2008)Stateless distributed algorithms for near optimal maximum multicommodity flowsProceedings of the twenty-seventh ACM symposium on Principles of distributed computing10.1145/1400751.1400835(440-440)Online publication date: 18-Aug-2008
https://dl.acm.org/doi/10.1145/1400751.1400835
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

Index Terms

Stateless near optimal flow control with poly-logarithmic convergence
1. Theory of computation
  1. Design and analysis of algorithms

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Information & Contributors

Information

Published In

cover image Guide Proceedings

LATIN'08: Proceedings of the 8th Latin American conference on Theoretical informatics

April 2008

794 pages

ISBN:3540787720

Editors:
Eduardo Sany Laber
PUC-RIO, Departamento de Informática, Gávea, Brazil
,
Claudson Bornstein
Universidade Federal do Rio de Janeiro, Departamento de Ciência da Computação, Rio de Janeiro, RJ, Brazil
,
Loana Tito Nogueira
Universidade Federal Fluminense, Instituto de Computação, Niterói, RJ, Brazil
,
Luerbio Faria
Universidade Estadual do Rio de Janeiro, São Gonçalo, RJ, Brazil

Sponsors

UOL
CAPES: Coordençãao de Aperfeiçoamento de Pessoal de Nível Superior
Microsoft: Microsoft
CNPq: Conselho Nacional de Desenvolvimento Cientifico e Tecn
FAPERJ: Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 07 April 2008

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Cited By

Allen-Zhu ZOrecchia LIndyk P(2015)Using optimization to break the epsilon barrierProceedings of the twenty-sixth annual ACM-SIAM symposium on Discrete algorithms10.5555/2722129.2722224(1439-1456)Online publication date: 4-Jan-2015
https://dl.acm.org/doi/10.5555/2722129.2722224
Awerbuch BKhandekar RBazzi RPatt-Shamir B(2008)Stateless distributed algorithms for near optimal maximum multicommodity flowsProceedings of the twenty-seventh ACM symposium on Principles of distributed computing10.1145/1400751.1400835(440-440)Online publication date: 18-Aug-2008
https://dl.acm.org/doi/10.1145/1400751.1400835
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

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