What approximation ratio can we achieve for the Facility Location problem if whenever a client u connects to facility v, opening cost of v is at most θ times service u? We show that this and many other problems are particular case Activation Edge-Cover problem. Here given multigraph G=(V,E), set R⊆V terminals, thresholds {tue,tve} each uv-edge e∈E. The goal find an assignment a={av:v∈V} nodes m...

We study the mechanism design problem of a social planner for locating two facilities on line interval [0, 1], where set n strategic agents report their locations and determines facilities. consider requirement minimum distance 0 ≤ d 1 between Given are heterogeneous, we model cost/utility an agent as sum his distances to both In heterogeneous two-facility location game minimize cost, show that...