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Scheduling Without Payments

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Abstract

We consider mechanisms without payments for the problem of scheduling unrelated machines. Specifically, we consider truthful in expectation randomized mechanisms under the assumption that a machine (player) is bound by its reports: when a machine lies and reports value \(\tilde{t}_{ij}\) for a task instead of the actual one t ij , it will execute for time \(\tilde{t}_{ij}\) if it gets the task (unless the declared value \(\tilde{t}_{ij}\) is less than the actual value t ij , in which case, it will execute for time t ij ). Our main technical result is an optimal mechanism for one task and n players which has approximation ratio (n+1)/2. We also provide a matching lower bound, showing that no other truthful mechanism can achieve a better approximation ratio. This immediately gives an approximation ratio of (n+1)/2 and n(n+1)/2 for social cost and makespan minimization, respectively, for any number of tasks. We also study the price of anarchy of natural algorithms.

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Notes

  1. We may also interpret the probabilities as fractional allocations. Naturally, our results apply to the fractional allocations as well.

  2. Proof: Let \(G(y)=\int_{0}^{y} g(x)\,dx\). Then

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Authors and Affiliations

  1. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK

    Elias Koutsoupias

  2. Department of Informatics and Telecommunications, University of Athens, Panepistimiopolis Ilissia, Athens, 15784, Greece

    Elias Koutsoupias

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  1. Elias Koutsoupias
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Correspondence to Elias Koutsoupias.

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Partially supported by the European Union Seventh Framework Programme FP7, grant 284731 (UaESMC), and by the ESF-NSRF research program Thales (AGT).

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Koutsoupias, E. Scheduling Without Payments. Theory Comput Syst 54, 375–387 (2014). https://doi.org/10.1007/s00224-013-9473-0

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