Heterogeneous Facility Location with Limited Resources

We initiate the study of heterogeneous facility location problem with limited resources. mainly focus on fundamental case where a set agents are positioned in line segment [0,1] and have approval preferences over two available facilities. A mechanism takes as input positions agents, chooses to locate single based this information. mechanisms that aim maximize social welfare (the total utility derive from facilities they approve), under constraint incentivizing truthfully report their preferences. consider three different settings depending level agent-related information is public or private. For each setting, we design deterministic randomized strategyproof achieve good approximation optimal welfare, complement these nearly-tight impossibility results.