On the multi-radius cover problem

An instance of the multi-radius cover problem consists of a graph G=(V,E) with edge lengths . Each vertex u∈V represents a transmission station for which a transmission radius ru must be picked. Edges represent a continuum of demand points to be satisfied, that is, for every edge (u,v)∈E we ask that ru+rv⩾luv. The cost of transmitting at radius r from vertex u is given by an arbitrary non-decreasing cost function cu(r). Our goal is to find a cover with minimum total cost ∑ucu(ru).The multi-radius cover problem is NP-hard as it generalizes the well-known vertex cover problem. In this paper we present a 2-approximation algorithm for it.