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Distributed selfish load balancing

Berenbrink, P.; Friedetzky, T.; Goldberg, L.A.; Goldberg, P.; Hu, Z.; Martin, R.

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Authors

P. Berenbrink

T. Friedetzky

L.A. Goldberg

P. Goldberg

Z. Hu

R. Martin



Abstract

Suppose that a set of m tasks are to be shared as equally as possible amongst a set of n resources. A game-theoretic mechanism to find a suitable allocation is to associate each task with a "selfish agent", and require each agent to select a resource, with the cost of a resource being the number of agents to select it. Agents would then be expected to migrate from overloaded to underloaded resources, until the allocation becomes balanced.Recent work has studied the question of how this can take place within a distributed setting in which agents migrate selfishly without any centralized control. In this paper we discuss a natural protocol for the agents which combines the following desirable features: It can be implemented in a strongly distributed setting, uses no central control, and has good convergence properties. For m ≫ n, the system becomes approximately balanced (an ε-Nash equilibrium) in expected time O(log log m). We show using a martingale technique that the process converges to a perfectly balanced allocation in expected time O(log log m + n4). We also give a lower bound of Ω (max{log log m, n}) for the convergence time.

Citation

Berenbrink, P., Friedetzky, T., Goldberg, L., Goldberg, P., Hu, Z., & Martin, R. (2007). Distributed selfish load balancing. SIAM Journal on Computing, 37(4), 1163-1181. https://doi.org/10.1137/060660345

Journal Article Type Article
Publication Date 2007-11
Deposit Date Oct 27, 2008
Publicly Available Date Mar 29, 2024
Journal SIAM Journal on Computing
Print ISSN 0097-5397
Electronic ISSN 1095-7111
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 37
Issue 4
Pages 1163-1181
DOI https://doi.org/10.1137/060660345
Keywords Task allocation, Nash equilibrium.

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