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Pricing for fairness: distributed resource allocation for multiple objectives

Published: 21 May 2006 Publication History

Abstract

In this paper, we present a simple distributed algorithm for resource allocation which simultaneously approximates the optimum value for a large class of objective functions. In particular, we consider the class of canonical utility functions U that are symmetric, non-decreasing, concave, and satisfy U(0) = 0. Our distributed algorithm is based on primal-dual updates. We prove that this algorithm is an O(log ρ)-approximation for all canonical utility functions simultaneously, i.e. without any knowledge of U. The algorithm needs at most O(log2 ρ) iterations. Here n is the number of flows, m is the number of edges, R is the ratio between the maximum capacity and the minimum capacity of the edges in the network, and ρ is max (n, m, R).We extend this result to multi-path routing, and also to a natural pricing mechanism that results in a simple and practical protocol for bandwidth allocation in a network. When the protocol reaches equilibrium, the allocated bandwidths are the same as when the distributed algorithm converges; hence the protocol is also an O(log ρ) approximation for all canonical utility functions.

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      cover image ACM Conferences
      STOC '06: Proceedings of the thirty-eighth annual ACM symposium on Theory of Computing
      May 2006
      786 pages
      ISBN:1595931341
      DOI:10.1145/1132516
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      Published: 21 May 2006

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      Author Tags

      1. fairness
      2. pricing
      3. primal-dual

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      May 21 - 23, 2006
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      • (2009)Bi-objective OptimizationProceedings of the 4th International Conference on Advances in Grid and Pervasive Computing10.1007/978-3-642-01671-4_21(223-234)Online publication date: 29-Apr-2009
      • (2008)Price based protocols for fair resource allocationProceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms10.5555/1347082.1347207(1145-1153)Online publication date: 20-Jan-2008
      • (2008)Fair welfare maximizationEconomic Theory10.1007/s00199-008-0406-041:3(465-494)Online publication date: 27-Aug-2008

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