Covering edges in networks

Abstract

AbstractIn this paper we consider the covering problem on a network G = (V, E) with edge demands. The task is to cover a subset J ⊆ E of the edges with a minimum number of facilities within a predefined coverage radius. We focus on both the nodal and the absolute version of this problem. In the latter, facilities may be placed everywhere in the network. While there already exist polynomial time algorithms to solve the problem on trees, we establish a finite dominating set (i.e., a finite subset of points provably containing an optimal solution) for the absolute version in general graphs. Complexity and approximability results are given and a greedy strategy is proved to be a (1 + ln(|J|))‐approximate algorithm. Finally, the different approaches are compared in a computational study.