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 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 non-negative 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. 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.