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 , 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 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.     

A 6.55 factor primal-dual approximation algorithm for the connected facility location problem

In the connected facility location (ConFL) problem, we are given a graph G=(V,E) with nonnegative edge cost c _e on the edges, a set of facilities ??V, a set of demands (i.e., clients) $\mathcal{D}\subseteq VIn the connected facility location (ConFL) problem, we are given a graph G=(V,E) with nonnegative edge cost c _e on the edges, a set of facilities ℱ⊆V, a set of demands (i.e., clients) D í V\mathcal{D}\subseteq V , and a parameter M≥1. Each facility i has a nonnegative opening cost f _i and each client j has d _j units of demand. Our objective is to open some facilities, say F⊆ℱ, assign each demand j to some open facility i(j)∈F and connect all open facilities using a Steiner tree T such that the total cost, which is ?_{i ? F}f_i+?_{j ? D}d_jc_i(j)j+M?_{e ? T}c_e\sum_{i\in F}f_{i}+\sum_{j\in \mathcal{D}}d_{j}c_{i(j)j}+M\sum_{e\in T}c_{e} , is minimized. We present a primal-dual 6.55-approximation algorithm for the ConFL problem which improves the previous primal-dual 8.55-approximation algorithm given by Swamy and Kumar (Algorithmica 40:245–269, 2004).