Localized Client-Server Load Balancing without Global Information

We consider distributed algorithms for maximizing throughput in a network of clients and servers, modeled as a bipartite graph. We seek algorithms and lower bounds for decentralized algorithms in which each participant has only local knowledge about the state of itself and its neighbors. Our problem...

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Bibliographic Details
Published in:SIAM journal on computing Vol. 37; no. 4; pp. 1259 - 1279
Main Authors: Awerbuch, Baruch, Hajiaghayi, Mohammad T., Kleinberg, Robert, Leighton, Tom
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2007
Subjects:
Algorithms
Applied mathematics
Competition
Computer science
Decision making
Laboratories
Scholarships & fellowships
Servers
ISSN:0097-5397, 1095-7111
Online Access:Get full text
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Summary:We consider distributed algorithms for maximizing throughput in a network of clients and servers, modeled as a bipartite graph. We seek algorithms and lower bounds for decentralized algorithms in which each participant has only local knowledge about the state of itself and its neighbors. Our problem is analogous to recent work on oblivious routing [M. Bienkowski, M. Korzeniowski, and H. Räcke, Proceedings of the $15$th Annual ACM Symposium on Parallel Algorithms and Architectures, 2003, pp. 24-33, C. Harrelson, K. Hildrum, and S. Rao, Proceedings of the $15$th Annual ACM Symposium on Parallel Algorithms and Architectures, 2003, pp. 34-43, H. Räcke, Proceedings of the $43$rd Annual IEEE Symposium on Foundations of Computer Science, 2002, pp. 43-52] but with the objective of maximizing throughput rather than minimizing congestion. In contrast to that work, we prove a strong lower bound (polynomial in $n$, the size of the graph) on the competitive ratio of any oblivious algorithm. This is accompanied by simple algorithms achieving upper bounds which are tight in terms of $\OPT$, the maximum throughput achievable by an omniscient algorithm, and are also tight in terms of $m$, the number of servers. Finally, we investigate an online version of the problem, in a restricted model which requires that clients, upon becoming active, must remain so for at least $log(n)$ time steps. In contrast to our primarily negative results in the oblivious case, here we present an algorithm which is constant-competitive. Our lower bounds justify the intuition, implicit in earlier work on the subject [B. Awerbuch and Y. Azar, Proceedings of the $35$th Annual IEEE Symposium on Foundations of Computer Science, 1994, pp. 240-249], that some such restriction (i.e., requiring some stability in the demand pattern over time) is necessary in order to achieve a constant--or even polylogarithmic--competitive ratio.
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ISSN:0097-5397
1095-7111
DOI:10.1137/S009753970444661X