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Bayesian Truthful Mechanisms for Job Scheduling from Bi-criterion Approximation Algorithms

Author(s)
Daskalakis, Konstantinos; Weinberg, Seth Matthew
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Abstract
We provide polynomial-time approximately optimal Bayesian mechanisms for makespan minimization on unrelated machines as well as for max-min fair allocations of indivisible goods, with approximation factors of 2 and min{m - k + 1, [~ over O](√k)} respectively, matching the approximation ratios of best known polynomial-time algorithms (for max-min fairness, the latter claim is true for certain ratios of the number of goods m to people k). Our mechanisms are obtained by establishing a polynomial-time approximation-sensitive reduction from the problem of designing approximately optimal mechanisms for some arbitrary objective O to that of designing bi-criterion approximation algorithms for the same objective O plus a linear allocation cost term. Our reduction is itself enabled by extending the celebrated “equivalence of separation and optimization” [27, 32] to also accommodate bi-criterion approximations. Moreover, to apply the reduction to the specific problems of makespan and max-min fairness we develop polynomial-time bi-criterion approximation algorithms for makespan minimization with costs and max-min fairness with costs, adapting the algorithms of [45], [10] and [4] to the type of bi-criterion approximation that is required by the reduction.
Date issued
2015
URI
http://hdl.handle.net/1721.1/99972
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Journal
Proceedings of the Twenty-sixth Annual ACM-SIAM Symposium on Discrete Algorithms
Publisher
Society for Industrial and Applied Mathematics
Citation
Daskalakis, Constantinos, and S. Matthew Weinberg. “Bayesian Truthful Mechanisms for Job Scheduling from Bi-Criterion Approximation Algorithms.” Proceedings of the Twenty-Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (December 22, 2014): 1934–1952.
Version: Original manuscript
ISBN
978-1-61197-374-7
978-1-61197-373-0

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