P. Berenbrink
Distributed selfish load balancing
Berenbrink, P.; Friedetzky, T.; Goldberg, L.A.; Goldberg, P.; Hu, Z.; Martin, R.
Authors
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 | Oct 27, 2008 |
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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