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Tighter price of anarchy for selfish task allocation on selfish machines

Author

Listed:
  • Xiayan Cheng

    (Hunan Normal University
    Hunan First Normal University)

  • Rongheng Li

    (Hunan Normal University)

  • Yunxia Zhou

    (Hunan Normal University)

Abstract

Given a set $$L = \{J_1,J_2,\ldots ,J_n\}$$L={J1,J2,…,Jn} of n tasks and a set $$M = \{M_1,M_2, \ldots ,M_m\}$$M={M1,M2,…,Mm} of m identical machines, in which tasks and machines are possessed by different selfish clients. Each selfish client of machine $$M_i \in M$$Mi∈M gets a profit equal to its load and each selfish client of task allocated to $$M_i$$Mi suffers from a cost equal to the load of $$M_i$$Mi. Our aim is to allocate the tasks on the m machines so as to minimize the maximum completion times of the tasks on each machine. A stable allocation is referred to as a dual equilibrium (DE). We firstly show that 4/3 is tight upper bound of the Price of Anarchy(PoA) with respect to dual equilibrium for $$m\in \{3,\ldots ,9\}$$m∈{3,…,9}. And secondly $$(7m-6)/(5m-3)$$(7m-6)/(5m-3) is an upper bound for $$m\ge 10$$m≥10. The result is better than the existing bound of 7/5.

Suggested Citation

  • Xiayan Cheng & Rongheng Li & Yunxia Zhou, 0. "Tighter price of anarchy for selfish task allocation on selfish machines," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-32.
    • Handle: RePEc:spr:jcomop:v::y::i::d:10.1007_s10878-020-00556-6
    DOI: 10.1007/s10878-020-00556-6
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    References listed on IDEAS

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    1. Nisan, Noam & Ronen, Amir, 2001. "Algorithmic Mechanism Design," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 166-196, April.
    2. Hui-Chih Hung & Bertrand M. T. Lin & Marc E. Posner & Jun-Min Wei, 2019. "Preemptive parallel-machine scheduling problem of maximizing the number of on-time jobs," Journal of Scheduling, Springer, vol. 22(4), pages 413-431, August.
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