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The Price of Anarchy for Minsum Related Machine Scheduling

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Approximation and Online Algorithms (WAOA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7164))

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Abstract

We address the classical uniformly related machine scheduling problem with minsum objective. The problem is solvable in polynomial time by the algorithm of Horowitz and Sahni. In that solution, each machine sequences its jobs shortest first. However when jobs may choose the machine on which they are processed, while keeping the same sequencing rule per machine, the resulting Nash equilibria are in general not optimal. The price of anarchy measures this optimality gap. By means of a new characterization of the optimal solution, we show that the price of anarchy in this setting is bounded from above by 2. We also give a lower bound of e/(e − 1) ≈ 1.58. This complements recent results on the price of anarchy for the more general unrelated machine scheduling problem, where the price of anarchy equals 4. Interestingly, as Nash equilibria coincide with shortest processing time first (SPT) schedules, the same bounds hold for SPT schedules. Thereby, our work also fills a gap in the literature.

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Authors and Affiliations

  1. Dept. Applied Mathematics, University of Twente, P.O. Box 217, 7500AE, Enschede, The Netherlands

    Ruben Hoeksma & Marc Uetz

Authors
  1. Ruben Hoeksma
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  2. Marc Uetz
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Editors and Affiliations

  1. Department of Computer Science, The University of Western Ontario, N6A 5B7, London, ON, Canada

    Roberto Solis-Oba

  2. Dipartimento di Informatica "Renato M. Capocelli", Università di Salerno, Via Ponte Don Melillo, 84081, Fisciano, SA, Italy

    Giuseppe Persiano

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Hoeksma, R., Uetz, M. (2012). The Price of Anarchy for Minsum Related Machine Scheduling. In: Solis-Oba, R., Persiano, G. (eds) Approximation and Online Algorithms. WAOA 2011. Lecture Notes in Computer Science, vol 7164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29116-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-29116-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29115-9

  • Online ISBN: 978-3-642-29116-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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