Improved Primal-Dual Approximation Algorithm for the Connected Facility Location Problem

Abstract

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 $\mathcal{F}\subset V$, a set of demands, i.e., clients $\mathcal{D}\subset V$, 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 $F\subset \mathcal{F}$, 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 $\sum_{i \in F} f_i + \sum_{j \in \mathcal D}d_jc_{i(j)j} + M \sum_{e \in T}c_e$, is minimized.

We give an improved primal-dual 6.55-approximation algorithm for the ConFL problem which improves the Swamy and Kumar’s primal-dual 8.55-approximation algorithm [1].

This research is supported by KOSEF Grant R01-2007-000-11905-0.