Approximation algorithms for connected facility location problems

We study Connected Facility Location problems. We are given a connected graph G=(V,E) with nonnegative edge cost c e for each edge e∈E, a set of clients D⊆V such that each client j∈D has positive demand d j and a set of facilities F⊆V each has nonnegative opening cost f i and capacity to serve all client demands. The objective is to open a subset of facilities, say $\hat{F}$ , 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 $\sum_{i\in \hat{F}}f_{i}+\sum_{j\in D}d_{j}c_{i(j)j}+M\sum_{e\in T}c_{e}$ is minimized for a given input parameter M≥1. We propose a LP-rounding based 8.29 approximation algorithm which improves the previous bound 8.55 (Swamy and Kumar in Algorithmica, 40:245–269, 2004). We also consider the problem when opening cost of all facilities are equal. In this case we give a 7.0 approximation algorithm.