Abstract
The state of the art in approximation algorithms for facility location problems are complicated combinations of various techniques. In particular, the currently best 1.488-approximation algorithm for the uncapacitated facility location (UFL) problem by Shi Li is presented as a result of a non-trivial randomization of a certain scaling parameter in the LP-rounding algorithm by Chudak and Shmoys combined with a primal-dual algorithm of Jain et al. In this paper we first give a simple interpretation of this randomization process in terms of solving an auxiliary (factor revealing) LP. Then, armed with this simple view point, we exercise the randomization on a more complicated algorithm for the k-level version of the problem with penalties in which the planner has the option to pay a penalty instead of connecting chosen clients, which results in an improved approximation algorithm.
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Byrka, J., Li, S., Rybicki, B. (2014). Improved Approximation Algorithm for k-Level UFL with Penalties, a Simplistic View on Randomizing the Scaling Parameter. In: Kaklamanis, C., Pruhs, K. (eds) Approximation and Online Algorithms. WAOA 2013. Lecture Notes in Computer Science, vol 8447. Springer, Cham. https://doi.org/10.1007/978-3-319-08001-7_8
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DOI: https://doi.org/10.1007/978-3-319-08001-7_8
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