New strategyproof mechanisms for distributed facility location problems

A new arXiv paper tackles the constrained distributed heterogeneous two-facility location problem using a max-variant cost model. In this setting, agents with private locations on a real line are split into disjoint groups. Facilities must be placed within a fixed multiset of candidate locations, each hosting at most one facility. The twist: an agent's individual cost is the distance to the farthest facility, not the nearest. The authors design strategyproof distributed mechanisms that operate in two stages. First, each group selects two candidate locations as representatives based solely on local reports. Then the mechanism chooses the final two facility locations from those representatives. The goal is to incentivize truthful reporting while approximating four social objectives: Average-of-Average, Max-of-Max, Average-of-Max, and Max-of-Average costs.

For each objective, the team proves constant lower and upper bounds on distortion—meaning the worst-case ratio between the mechanism's social cost and the optimal social cost is bounded by a fixed constant. This is a significant theoretical contribution to the field of algorithmic game theory, as it provides provable guarantees for distributed decision-making without a central authority. The results apply to scenarios like placing public facilities (e.g., fire stations or Wi-Fi hotspots) where agents are organized into communities and must report their preferences truthfully despite conflicting interests. By combining distributed computing constraints with strategyproofness, the work bridges a gap between mechanism design and real-world location planning.