Fault-Tolerant Facility Location: A Randomized Dependent LP-Rounding Algorithm

Abstract

We give a new randomized LP-rounding 1.725-approximation algorithm for the metric Fault-Tolerant Uncapacitated Facility Location problem. This improves on the previously best known 2.076-approximation algorithm of Swamy & Shmoys. To the best of our knowledge, our work provides the first application of a dependent-rounding technique in the domain of facility location. The analysis of our algorithm benefits from, and extends, methods developed for Uncapacitated Facility Location; it also helps uncover new properties of the dependent-rounding approach.

An important concept that we develop is a novel, hierarchical clustering scheme. Typically, LP-rounding approximation algorithms for facility location problems are based on partitioning facilities into disjoint clusters and opening at least one facility in each cluster. We extend this approach and construct a laminar family of clusters, which then guides the rounding procedure: this allows us to exploit properties of dependent rounding, and provides a quite tight analysis resulting in the improved approximation ratio.

This work was partially supported by: (i) the Future and Emerging Technologies Unit of EC (IST priority - 6th FP), under contract no. FP6-021235-2 (project ARRIVAL), (ii) MNISW grant number N N206 1723 33, 2007–2010, (iii) NSF ITR Award CNS-0426683 and NSF Award CNS-0626636, and (iv) NSERC grant 327620-09 and an Ontario Early Researcher Award.