1,686 research outputs found
Heterogeneous Facility Location with Limited Resources
We initiate the study of the heterogeneous facility location problem with limited resources. We mainly focus on the fundamental case where a set of agents are positioned in the line segment [0,1] and have approval preferences over two available facilities. A mechanism takes as input the positions and the preferences of the agents, and chooses to locate a single facility based on this information. We study mechanisms that aim to maximize the social welfare (the total utility the agents derive from facilities they approve), under the constraint of incentivizing the agents to truthfully report their positions and preferences. We consider three different settings depending on the level of agent-related information that is public or private. For each setting, we design deterministic and randomized strategyproof mechanisms that achieve a good approximation of the optimal social welfare, and complement these with nearly-tight impossibility results
Nash Welfare and Facility Location
We consider the problem of locating a facility to serve a set of agents
located along a line. The Nash welfare objective function, defined as the
product of the agents' utilities, is known to provide a compromise between
fairness and efficiency in resource allocation problems. We apply this welfare
notion to the facility location problem, converting individual costs to
utilities and analyzing the facility placement that maximizes the Nash welfare.
We give a polynomial-time approximation algorithm to compute this facility
location, and prove results suggesting that it achieves a good balance of
fairness and efficiency. Finally, we take a mechanism design perspective and
propose a strategy-proof mechanism with a bounded approximation ratio for Nash
welfare
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