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.
This research was supported by the project Algorithmic Game Theory, co-financed by the European Union (European Social Fund - ESF) and Greek national funds, through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) - Research Funding Program: THALES, investing in knowledge society through the European Social Fund. Full version at http://arxiv.org/abs/1207.0935
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Fotakis, D., Tzamos, C. (2013). On the Power of Deterministic Mechanisms for Facility Location Games. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39206-1_38
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