The VCG Mechanism for Bayesian Scheduling

  • Yiannis Giannakopoulos
  • Maria Kyropoulou
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9470)


We study the problem of scheduling m tasks to n selfish, unrelated machines in order to minimize the makespan, where 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 \(O\left( \frac{\ln n}{\ln \ln n}\right) \). This improves significantly on the previously best known bound of \(O\left( \frac{m}{n}\right) \) for prior-independent mechanisms, given by Chawla et al. [STOC’13] under the additional assumption of Monotone Hazard Rate (MHR) distributions. Although we demonstrate that this is in general tight, if we do maintain the MHR assumption, then we get improved, (small) constant bounds for \(m\ge n\ln n\) i.i.d. tasks, while we also identify a sufficient condition on the distribution that yields a constant approximation ratio regardless of the number of tasks.


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© Springer-Verlag Berlin Heidelberg 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.University of LiverpoolLiverpoolUK
  2. 2.University of OxfordOxfordUK

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