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Mechanisms for Scheduling with Single-Bit Private Values

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Abstract

We study the problem of designing truthful mechanisms for makespan minimization in scheduling. In particular, we consider randomized mechanisms for a restriction of the general multi-dimensional domain (i.e., unrelated machines). In a sense, our setting is the simplest multi-dimensional setting, where each machine holds privately only a single-bit of information. Some of the impossibility results for deterministic mechanisms carry over our setting as well. We prove a separation between truthful-in-expectation and universally truthful mechanisms for makespan minimization: We first show how to design an optimal truthful-in-expectation mechanism, and then prove lower bounds on the approximation guarantee of universally truthful mechanisms.

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Notes

  1. Notice that the information missing is just a single bit, much less than that of the related machines case, where the missing information is a positive real number. However, ours is not a single-dimensional domain. We refer the reader to Chapter 9 and 12 of [18] for the precise definition of a single-dimensional domain.

  2. Notice that such a separation was not known for the general problem since, although Lu [14], showed a lower bound higher than 1.5 for universally truthful mechanisms, the result holds only for scale-free mechanisms. This is arguably a very natural assumption, but it is still needed to be proven that it is without loss of generality.

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Acknowledgments

Part of this work was done while the second author was at the Max-Planck Institute for Informatics, Saarbrücken, while visiting the Università di Salerno, and was also supported by EPSRC grant EP/K01000X/1. Research of the first author partially supported by the PRIN 2011 research project ARS TechnoMedia – Algorithmics for Social Technological Networks, funded by the Italian Ministry of University and Research.

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Authors and Affiliations

  1. Dipartimento di Informatica, Università di Salerno, Salerno, Italy

    Vincenzo Auletta & Paolo Penna

  2. Computer Science Department, University of Liverpool, Liverpool, UK

    George Christodoulou

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  1. Vincenzo Auletta
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  2. George Christodoulou
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  3. Paolo Penna
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Correspondence to Vincenzo Auletta.

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Auletta, V., Christodoulou, G. & Penna, P. Mechanisms for Scheduling with Single-Bit Private Values. Theory Comput Syst 57, 523–548 (2015). https://doi.org/10.1007/s00224-015-9625-5

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