(Almost) optimal coordination mechanisms for unrelated machine scheduling

Yossi Azar, Kamal Jain, Vahab Mirrokni

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We investigate the influence of different algorithmic choices on the approximation ratio in selfish scheduling. Our goal is to design local policies that minimize the inefficiency of resulting equilibria. In particular, we design optimal coordination mechanisms for unrelated machine scheduling, and improve the known approximation ratio from Θ(m) to Θ(log m), where m is the number of machines. A local policy for each machine orders the set of jobs assigned to it only based on parameters of those jobs. A strongly local policy only uses the processing time of jobs on the the same machine. We prove that the approximation ratio of any set of strongly local ordering policies in equilibria is at least Ω(m). In particular, it implies that the approximation ratio of a greedy shortest-first algorithm for machine scheduling is at least Ω(m). This closes the gap between the known lower and upper bounds for this problem, and answers an open question raised by Ibarra and Kim[16], and Davis and Jaffe[10]. We then design a local ordering policy with the approximation ratio of Θ(log m) in equilibria, and prove that this policy is optimal among all local ordering policies. This policy orders the jobs in the non-decreasing order of their inefficiency, i.e, the ratio between the processing time on that machine over the minimum processing time. Finally, we show that best responses of players for the inefficiency-based policy may not converge to a pure Nash equilibrium, and present a Θ(log2 m) policy for which we can prove fast convergence of best responses to pure Nash equilibria.

Original languageEnglish
Title of host publicationProceedings of the 19th Annual ACM-SIAM Symposium on Discrete Algorithms
PublisherAssociation for Computing Machinery
Pages323-332
Number of pages10
ISBN (Print)9780898716474
StatePublished - 2008
Externally publishedYes
Event19th Annual ACM-SIAM Symposium on Discrete Algorithms - San Francisco, CA, United States
Duration: 20 Jan 200822 Jan 2008

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Conference

Conference19th Annual ACM-SIAM Symposium on Discrete Algorithms
Country/TerritoryUnited States
CitySan Francisco, CA
Period20/01/0822/01/08

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