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. © 2010 Springer-Verlag.
CITATION STYLE
Byrka, J., Srinivasan, A., & Swamy, C. (2010). Fault-tolerant facility location: A randomized dependent LP-rounding algorithm. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6080 LNCS, pp. 244–257). https://doi.org/10.1007/978-3-642-13036-6_19
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