Fault Tolerant Clustering Revisited

TL;DR

This paper presents simple, practical constant-factor approximation algorithms for fault-tolerant k-center and k-median clustering problems, where points are assigned to their -th nearest center instead of the nearest, improving robustness in clustering.

Contribution

It introduces the first simple, practical constant-factor approximation algorithms for fault-tolerant k-center and k-median clustering problems.

Findings

Algorithms achieve constant-factor approximation guarantees.

Methods are conceptually simple and easy to implement.

Applicable to fault-tolerant clustering scenarios in metric spaces.

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.