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

Jaroslaw Byrka, Aravind Srinivasan, Chaitanya Swamy
2010 Lecture Notes in Computer Science  
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
more » ... over 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. It allows to exploit properties of dependent rounding, and provides a quite tight analysis resulting in the improved approximation ratio.
doi:10.1007/978-3-642-13036-6_19 fatcat:zxbh76qkfjevjno4npvs3mo3r4