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The cost of selfishness for maximizing the minimum load on uniformly related machines

Author

Listed:
  • Leah Epstein

    (University of Haifa)

  • Elena Kleiman

    (University of Haifa)

  • Rob Stee

    (Max-Planck-Institut für Informatik)

Abstract

Consider the following scheduling game. A set of jobs, each controlled by a selfish agent, are to be assigned to m uniformly related machines. The cost of a job is defined as the total load of the machine that its job is assigned to. A job is interested in minimizing its cost, while the social objective is maximizing the minimum load (the value of the cover) over the machines. This goal is different from the regular makespan minimization goal, which was extensively studied in a game theoretic context. We study the price of anarchy (poa) and the price of stability (pos) for uniformly related machines. The results are expressed in terms of s, which is the maximum speed ratio between any two machines. For uniformly related machines, we prove that the pos is unbounded for s>2, and the poa is unbounded for s≥2. For the remaining cases we show that while the poa grows to infinity as s tends to 2, the pos is at most 2 for any s≤2.

Suggested Citation

  • Leah Epstein & Elena Kleiman & Rob Stee, 2014. "The cost of selfishness for maximizing the minimum load on uniformly related machines," Journal of Combinatorial Optimization, Springer, vol. 27(4), pages 767-777, May.
    • Handle: RePEc:spr:jcomop:v:27:y:2014:i:4:d:10.1007_s10878-012-9555-y
    DOI: 10.1007/s10878-012-9555-y
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    References listed on IDEAS

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    1. Petra Schuurman & Tjark Vredeveld, 2007. "Performance Guarantees of Local Search for Multiprocessor Scheduling," INFORMS Journal on Computing, INFORMS, vol. 19(1), pages 52-63, February.
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    Cited by:

    1. Deshi Ye & Lin Chen & Guochuan Zhang, 2021. "On the price of anarchy of two-stage machine scheduling games," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 616-635, October.
    2. Deshi Ye & Lin Chen & Guochuan Zhang, 0. "On the price of anarchy of two-stage machine scheduling games," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-20.

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