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arXiv · 1307.2520

Fault Tolerant Clustering Revisited

Nirman Kumar·Benjamin Raichel
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Abstract

In discrete k-center and k-median clustering, we are given a set of points P in a metric space M, and the task is to output a set C \subseteq ? P, |C| = k, such that the cost of clustering P using C is as small as possible. For k-center, the cost is the furthest a point has to travel to its nearest center, whereas for k-median, the cost is the sum of all point to nearest center distances. In the fault-tolerant versions of these problems, we are given an additional parameter 1 ?\leq \ell \leq ? k, such that when computing the cost of clustering, points are assigned to their \ell-th nearest-neighbor in C, instead of their nearest neighbor. We provide constant factor approximation algorithms for these problems that are both conceptually simple and highly practical from an implementation stand-point.

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Nirman Kumar, Benjamin Raichel. 2013-07-09. Fault Tolerant Clustering Revisited. https://arxiv.org/abs/1307.2520

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