LATIN 2016: LATIN 2016: Theoretical Informatics pp 441-453

# Improved Approximation Algorithms for Capacitated Fault-Tolerant k-Center

• Cristina G. Fernandes
• Samuel P. de Paula
• Lehilton L. C. Pedrosa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)

## Abstract

In the k-center problem, given a metric space V and a positive integer k, one wants to select k elements (centers) of V and an assignment from V to centers, minimizing the maximum distance between an element of V and its assigned center. One of the most general variants is the capacitated $$\alpha$$ -fault-tolerant k -center, where centers have a limit on the number of assigned elements, and, if $$\alpha$$ centers fail, there is a reassignment from V to non-faulty centers. In this paper, we present a new approach to tackle fault tolerance, by selecting and pre-opening a set of backup centers, then solving the obtained residual instance. For the $$\{0,L\}$$-capacitated case, we give approximations with factor 6 for the basic problem, and 7 for the so called conservative variant, when only clients whose centers failed may be reassigned. Our algorithms improve on the previously best known factors of 9 and 17, respectively. Moreover, we consider the case with general capacities. Assuming $$\alpha$$ is constant, our method leads to the first approximations for this case.

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## Authors and Affiliations

• Cristina G. Fernandes
• 1
• Samuel P. de Paula
• 1
• Lehilton L. C. Pedrosa
• 2
Email author
1. 1.Department of Computer ScienceUniversity of São PauloSão PauloBrazil
2. 2.Institute of ComputingUniversity of CampinasCampinasBrazil