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We study the impact on mechanisms for facility location of moving from one dimension to two (or more) dimensions and Euclidean or Manhattan distances.
On strategy-proofness and single peakedness
Moulin, H. 1980 · 1980
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Linear-time algorithms for linear programming in R3 and related problems
Megiddo, N. 1982 · 1982
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Pareto Optimality, Anonymity, and Strategy-Proofness in Location Problems
Peters, H.; van der Stel, H.; and Storcken, T. 1992 · 1992
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Generalized Median Voter Schemes and Committees
Barberà, S.; Gul, F.; and Stacchetti, E. 1993 · 1993
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The Capacitated p-facility Location Problem on the Real Line
Brimberg, J.; Korach, E.; Eben-Chaim, M.; and Mehrez, A. 2001 · 2001
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Facility Location: Applications and Theory
Drezner, Z.; and Hamacher, H., eds. 2002 · 2002
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Winner-Imposing Strategyproof Mechanisms for Multiple Facility Location Games
Fotakis, D.; and Tzamos, C. 2010 · 2010
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Strategy-Proof Mechanisms for Facility Location Games with Many Facilities
Escoffier, B.; Gourvès, L.; Thang, N. K.; Pascual, F.; and Spanjaard, O. 2011 · 2011
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On the Power of Deterministic Mechanisms for Facility Location Games
Fotakis, D.; and Tzamos, C. 2013 · 2013
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Approximate Mechanism Design Without Money
Procaccia, A.; and Tennenholtz, M. 2013 · 2013
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Analysis and Optimization of Multi-Dimensional Percentile Mechanisms
Sui, X.; Boutilier, C.; and Sandholm, T. 2013 · 2013
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Strategyproof Mechanisms for One-Dimensional Hybrid and Obnoxious Facility Location Models
Feigenbaum, I.; and Sethuraman, J. 2015 · 2015
Deep Learning for Multi-Facility Location Mechanism Design
Golowich, N.; Narasimhan, H.; and Parkes, D. 2018 · 2018
Later among the works it cites.
The Capacity Constrained Facility Location Problem
Aziz, H.; Chan, H.; Lee, B. E.; and Parkes, D. C. 2019 · 2019
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Facility Location Problem with Capacity Constraints: Algorithmic and Mechanism Design Perspectives
Aziz, H.; Chan, H.; Lee, B.; Li, B.; and Walsh, T. 2020 · 2020
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Coordinate-wise Median: Not Bad, Not Bad, Pretty Good
Goel, S.; and Hann-Caruthers, W. 2020 · 2020
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Strategy Proof Mechanisms for Facility Location with Capacity Limits
Anonymous. 2021 · 2021
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Cited alongside, same era.