THE P MAXIMAL COVER - P PARTIAL CENTER PROBLEM ON NETWORKS

The p maximal cover problem is to find a set of locations for p facilities so as to maximize the total demand (covered) that is at most T units away from a closest facility. The p partial center problem is to find a set of locations for the p facilities that minimizes the maximum distance between a closest facility and the demand covered. In this paper we show the relationship between the two problems on networks. For a tree network with one facility we present an algorithm to obtain all Pareto locations with respect to the two objectives: maximum cover and minimax distance. For general networks we discuss the p maximal cover problem requiring that the optimal solution is a Pareto location.