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On the Power of Deterministic Mechanisms for Facility Location Games

  • Dimitris Fotakis
  • Christos Tzamos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7965)

Abstract

We investigate the approximability of K-Facility Location by deterministic strategyproof mechanisms. Our main result is an elegant characterization of deterministic strategyproof mechanisms with a bounded approximation ratio for 2-Facility Location on the line. Specifically, we show that for instances with n ≥ 5 agents, any such mechanism either admits a unique dictator, or always places the facilities at the two extremes. As a consequence, we obtain that the best approximation ratio achievable by deterministic strategyproof mechanisms for 2-Facility Location on the line is precisely n − 2. Employing a technical tool developed for the characterization, we show that for every K ≥ 3, there do not exist any deterministic anonymous strategyproof mechanisms with a bounded approximation ratio for K-Facility Location on the line, even for simple instances with K + 1 agents. Moreover, building on the characterization for the line, we show that there do not exist any deterministic mechanisms with a bounded approximation ratio for 2-Facility Location in more general metric spaces, which is true even for simple instances with 3 agents located in a star.

Keywords

Social Choice Approximation Ratio General Metrics Prefer Agent Deterministic Mechanism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dimitris Fotakis
    • 1
  • Christos Tzamos
    • 2
  1. 1.School of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece
  2. 2.Computer Science and Artificial Intelligence LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

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