Approximate Mechanism Design for Distributed Facility Location

We consider a single-facility location problem, where agents are positioned on the real line and partitioned into multiple disjoint districts. The goal is to choose (where public facility be built) so as minimize total distance of from it. This process distributed: positions in each district first aggregated representative for district, then one representatives chosen location. indirect access inevitably leads inefficiency, which captured by notion distortion. study discrete version set alternative locations finite, well continuous one, every point an alternative, paint almost complete picture distortion landscape both general strategyproof distributed mechanisms.