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The VCG Mechanism for Bayesian Scheduling

The VCG Mechanism for Bayesian Scheduling We study the problem of scheduling m tasks to n selfish, unrelated machines in order to minimize the makespan, in which the execution times are independent random variables, identical across machines. We show that the VCG mechanism, which myopically allocates each task to its best machine, achieves an approximation ratio of O(ln n ln / ln n). This improves significantly on the previously best known bound of O(m/n) for prior-independent mechanisms, given by Chawla et al. [7] under the additional assumption of Monotone Hazard Rate (MHR) distributions. Although we demonstrate that this is tight in general, if we do maintain the MHR assumption, then we get improved, (small) constant bounds for m ≥ n ln n i.i.d. tasks. We also identify a sufficient condition on the distribution that yields a constant approximation ratio regardless of the number of tasks. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Economics and Computation (TEAC) Association for Computing Machinery

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References (43)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2017 ACM
ISSN
2167-8375
eISSN
2167-8383
DOI
10.1145/3105968
Publisher site
See Article on Publisher Site

Abstract

We study the problem of scheduling m tasks to n selfish, unrelated machines in order to minimize the makespan, in which the execution times are independent random variables, identical across machines. We show that the VCG mechanism, which myopically allocates each task to its best machine, achieves an approximation ratio of O(ln n ln / ln n). This improves significantly on the previously best known bound of O(m/n) for prior-independent mechanisms, given by Chawla et al. [7] under the additional assumption of Monotone Hazard Rate (MHR) distributions. Although we demonstrate that this is tight in general, if we do maintain the MHR assumption, then we get improved, (small) constant bounds for m ≥ n ln n i.i.d. tasks. We also identify a sufficient condition on the distribution that yields a constant approximation ratio regardless of the number of tasks.

Journal

ACM Transactions on Economics and Computation (TEAC)Association for Computing Machinery

Published: Dec 14, 2017

Keywords: Bayesian mechanism design

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