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Fair Cost-Sharing Methods for Scheduling Jobs on Parallel Machines

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Algorithms and Complexity (CIAC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3998))

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Abstract

We consider the problem of sharing the cost of scheduling n jobs on m parallel machines among a set of agents. In our setting, each agent owns one job and the cost is given by the makespan of the computed assignment. We focus on α-budget-balanced cross-monotonic cost-sharing methods since they guarantee the two substantial mechanism properties α-budget-balance and group-strategyproofness and provide fair cost-shares. For identical jobs on related machines and for arbitrary jobs on identical machines, we give (m+1)/(2m)-budget-balanced cross-monotonic cost-sharing methods and show that this is the best approximation possible. As our major result, we prove that the approximation factor for cross-monotonic cost-sharing methods is unbounded for arbitrary jobs and related machines. We therefore develop a cost-sharing method in the (m+1)/(2m)-core, a weaker but also fair solution concept. We close with a strategyproof mechanism for the model of arbitrary jobs and related machines that recovers at least 3/5 of the cost. All given solutions can be computed in polynomial time.

This work has been partially supported by the German Science Foundation (DFG) priority program 1126 Algorithms of Large and Complex Networks under grant MO 285/15-3, and by the European Union within the 6th Framework Programme under contract 001907 (DELIS).

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Author information

Authors and Affiliations

  1. Faculty of Computer Science, Electrical Engineering and Mathematics, University of Paderborn, Fürstenallee 11, 33102, Paderborn, Germany

    Yvonne Bleischwitz & Burkhard Monien

  2. International Graduate School of Dynamic Intelligent Systems,  

    Yvonne Bleischwitz

Authors
  1. Yvonne Bleischwitz
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  2. Burkhard Monien
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Rome, ”Sapienza”, Italy

    Tiziana Calamoneri

  2. Computer Science Department, Sapienza University of Rome, Via Salaria, 113, 00198, Rome, Italy

    Irene Finocchi

  3. Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Roma, Italy

    Giuseppe F. Italiano

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Bleischwitz, Y., Monien, B. (2006). Fair Cost-Sharing Methods for Scheduling Jobs on Parallel Machines. In: Calamoneri, T., Finocchi, I., Italiano, G.F. (eds) Algorithms and Complexity. CIAC 2006. Lecture Notes in Computer Science, vol 3998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758471_19

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  • DOI: https://doi.org/10.1007/11758471_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34375-2

  • Online ISBN: 978-3-540-34378-3

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