Nicolas Fröhlich, Andrea Maier, Horst W. Hamacher

• In this paper we consider the covering problem on a networkG=(V,E)withedgedemands. The task is to cover a subsetJ⊆Eof the edges with a minimum numberof facilities within a predefined coverage radius. We focus on both the nodal andthe absolute version of this problem. In the latter, facilities may be placed every-where in the network. While there already exist polynomial time algorithms to solvethe problem on trees, we establish a finite dominating set (i.e., a finite subset ofpoints provably containing an optimal solution) for the absolute version in generalgraphs. Complexity and approximability results are given and a greedy strategy isproved to be a (1+ln(|J|))-approximate algorithm. Finally, the different approachesare compared in a computational study.