Improved approximation algorithm for connected facility location problems

Abstract

We study the Connected Facility Location problems. We are given a connected graph G = (V, E) with non-negative edge cost ce for each edge e € E, a set of clients D ⊆ V such that each client j € D has positive demand d¡ and a set of facilities F ⊆ V each has non-negative opening cost fi and capacity to serve all client demands. The objective is to open a subset of facilities, say F̂, to assign each client j € D to exactly one open facility i(j) and to connect all open facilities by a Steiner tree T such that the cost Σ i€F̂ fi + Σj€D d jci(j)j+ M Σe€Tce is minimized. We propose a LP-rounding based 8.29 approximation algorithm which improves the previous bound 8.55. We also consider the problem when opening cost of all facilities are equal. In this case we give a 7.0 approximation algorithm. © Springer-Verlag Berlin Heidelberg 2007.