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Coordination Mechanisms, Cost-Sharing, and Approximation Algorithms for Scheduling

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Web and Internet Economics (WINE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10660))

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Abstract

We reveal a connection between coordination mechanisms for unrelated machine scheduling and cost-sharing protocols. Using this connection, we interpret three coordination mechanisms from the recent literature as Shapley-value-based cost-sharing protocols, thus providing a unifying justification regarding why these mechanisms induce potential games. More importantly, this connection provides a template for designing novel coordination mechanisms, as well as approximation algorithms for the underlying optimization problem. The designer need only decide the total cost to be suffered on each machine, and then the Shapley value can be used to induce games guaranteed to possess a potential function; these games can, in turn, be used to design algorithms. To verify the power of this approach, we design a combinatorial algorithm that achieves an approximation guarantee of 1.81 for the problem of minimizing the total weighted completion time for unrelated machines. To the best of our knowledge, this is the best approximation guarantee among combinatorial polynomial-time algorithms for this problem.

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Notes

  1. 1.

    Note that computing the Shapley value cost-shares can be non-trivial, or even intractable, if the \(C_i(J_i)\) is arbitrarily general, but most of the natural choices for this function provide sufficient structure for the shares to be readily computable, as verified in the previous and the following section.

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Author information

Authors and Affiliations

  1. University of Patras, Rion-Patras, Greece

    Ioannis Caragiannis

  2. Drexel University, Philadelphia, PA, USA

    Vasilis Gkatzelis

  3. Gran Sasso Science Institute, L’Aquila, Italy

    Cosimo Vinci

Authors
  1. Ioannis Caragiannis
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  2. Vasilis Gkatzelis
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  3. Cosimo Vinci
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Corresponding author

Correspondence to Ioannis Caragiannis .

Editor information

Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Nikhil R. Devanur

  2. Shanghai University of Finance and Economics, Shanghai, China

    Pinyan Lu

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Caragiannis, I., Gkatzelis, V., Vinci, C. (2017). Coordination Mechanisms, Cost-Sharing, and Approximation Algorithms for Scheduling. In: R. Devanur, N., Lu, P. (eds) Web and Internet Economics. WINE 2017. Lecture Notes in Computer Science(), vol 10660. Springer, Cham. https://doi.org/10.1007/978-3-319-71924-5_6

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  • DOI: https://doi.org/10.1007/978-3-319-71924-5_6

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  • Online ISBN: 978-3-319-71924-5

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