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The price of envy-freeness in machine scheduling

Author

Listed:
  • Vittorio Bilò

    (University of Salento [Lecce], Department of Mathematics and Physics - University of Salento [Lecce])

  • Angelo Fanelli

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Michele Flammini

    (DISIM - Department of Information Engineering, Computer Science and Mathematics = Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila] - UNIVAQ - Università degli Studi dell'Aquila = University of L'Aquila)

  • Gianpiero Monaco

    (DISIM - Department of Information Engineering, Computer Science and Mathematics = Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica [L'Aquila] - UNIVAQ - Università degli Studi dell'Aquila = University of L'Aquila)

  • Luca Moscardelli

    (Dipartimento di Scienze - Universita di Chieti-Pescara - UNICH - Universita' degli Studi "G. d'Annunzio" Chieti-Pescara)

Abstract

We consider k-envy-free assignments for scheduling problems in which the completion time of each machine is not k times larger than the one she could achieve by getting the jobs of another machine, for a given factor . We introduce and investigate the notion of price of k-envy-freeness, defined as the ratio between the makespan of the best k-envy-free assignment and that of an optimal allocation achievable without envy-freeness constraints. We provide exact or asymptotically tight bounds on the price of k-envy-freeness for all the basic scheduling models, that is unrelated, related and identical machines. Moreover, we show how to efficiently compute such allocations with a worsening multiplicative factor being at most the best approximation ratio for the minimum makespan problem guaranteed by a polynomial time algorithm for each specific model. Finally, we extend our results to the case of restricted assignments and to the objective of minimizing the sum of the completion times of all the machines.

Suggested Citation

  • Vittorio Bilò & Angelo Fanelli & Michele Flammini & Gianpiero Monaco & Luca Moscardelli, 2016. "The price of envy-freeness in machine scheduling," Post-Print hal-02089421, HAL.
    • Handle: RePEc:hal:journl:hal-02089421
    DOI: 10.1016/j.tcs.2015.10.046
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    Keywords

    Envy-freeness; Machine scheduling;

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