# Fault tolerant clustering revisited

## Abstract

In discrete κ-center and κ-median clustering, we are given a set of points P in a metric space M, and the task is to output a set C ⊆ P, |C| = κ, 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 ≤ ≤ k, such that when computing the cost of clustering, points are assigned to their lth 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.

## Publication Title

CCCG 2013 - 25th Canadian Conference on Computational Geometry

## Recommended Citation

Kumar, N., & Raichel, B.
(2013). Fault tolerant clustering revisited.* CCCG 2013 - 25th Canadian Conference on Computational Geometry*, 103-108.
Retrieved from https://digitalcommons.memphis.edu/facpubs/2825