Optimal Lower Bounds for Anonymous Scheduling Mechanisms
Name
Ashlagi_Optimal lower.pdf
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489.59 KB
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Author(s)
Ashlagi, Itai
Dobzinski, Shahar
Lavi, Ron
Date Issued
May 2012
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Ashlagi, Itai, Shahar Dobzinski, and Ron Lavi. “Optimal Lower Bounds for Anonymous Scheduling Mechanisms.” Mathematics of Operations Research 37, no. 2 (May 2012): 244–258.
Version
Author's final manuscript
Abstract
We consider the problem of designing truthful mechanisms on m unrelated machines, to minimize some optimization goal. Nisan and Ronen [Nisan, N., A. Ronen. 2001. Algorithmic mechanism design. Games Econom. Behav. 35 166–196] consider the specific goal of makespan minimization, and show a lower bound of 2, and an upper bound of m. This large gap inspired many attempts that yielded positive results for several special cases, but very partial success for the general case: the lower bound was slightly increased to 2.61 by Christodoulou et al. [Christodoulou, G., E. Koutsoupias, A. Kovács. 2010. Mechanism design for fractional scheduling on unrelated machines. ACM Trans. Algorithms (TALG) 6(2) 1–18] and Koutsoupias and Vidali [Koutsoupias, E., A. Vidali. 2007. A lower bound of 1+phi for truthful scheduling mechanisms. Proc. 32nd Internat. Sympos. Math. Foundations Comput. Sci. (MFCS)], while the best upper bound remains unchanged. In this paper we show the optimal lower bound on truthful anonymous mechanisms: no such mechanism can guarantee an approximation ratio better than m. Moreover, our proof yields similar optimal bounds for two other optimization goals: the sum of completion times and the lp norm of the schedule.
MIT Department
Sloan School of Management
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DOI of Published Version
https://doi.org/10.1287/moor.1110.0534
