Fault Tolerant Clustering Revisited
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.
Cite
@article{arxiv.1307.2520,
title = {Fault Tolerant Clustering Revisited},
author = {Nirman Kumar and Benjamin Raichel},
journal= {arXiv preprint arXiv:1307.2520},
year = {2013}
}