# Primal-Dual Algorithms for Connected Facility Location Problems

• Chaitanya Swamy
• Amit Kumar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2462)

## Abstract

We consider the Connected Facility Location problem. We are given a graph G = (V,E) with cost c e on edge e, a set of facilities FV, and a set of demands DV. We are also given a parameter M ≥ 1. A solution opens some facilities, say F, assigns each demand j to an open facility i(j), and connects the open facilities by a Steiner tree T. The cost incurred is $$\sum {_{i \in F} f_i } + \sum {_{j \in \mathcal{D}} d_j c_{i\left( j \right)j} } + M\sum {_{e \in T} c_e }$$ . We want a solution of minimum cost. A special case is when all opening costs are 0 and facilities may be opened anywhere, i.e.,F = V. If we know a facility v that is open, then this problem reduces to the rent-or-buy problem. We give the first primal-dual algorithms for these problems and achieve the best known approximation guarantees. We give a 9-approximation algorithm for connected facility location and a 5-approximation for the rent-or-buy problem. Our algorithm integrates the primal-dual approaches for facility location [7] and Steiner trees [1],[2]. We also consider the connected k-median problem and give a constant-factor approximation by using our primal-dual algorithm for connected facility location. We generalize our results to an edge capacitated version of these problems.

## Keywords

Facility Location Steiner Tree Facility Location Problem Demand Point Network Design Problem
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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