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Fast Clustering with Lower Bounds: No Customer too Far, No Shop too Small by Ene, Alina; Har-Peled, Sariel; Raichel, Benjamin is a scholarly article available to read on EtoBox.

What is Fast Clustering with Lower Bounds: No Customer too Far, No Shop too Small about?

We study the \LowerBoundedCenter (\lbc) problem, which is a clustering problem that can be viewed as a variant of the \kCenter problem. In the \lbc problem, we are given a set of points P in a metric space and a lower bound \lambda, and the goal is to select a set C \subseteq P of centers and an assignment that maps each point in P to a center of C such that each center of C is assigned at least \lambda points. The price of an assignment is the maximum distance between a point and the center it is assigned to, and the goal is to find a set of centers and an assignment of minimum price. We give a constant factor approximation algorithm for the \lbc problem that runs in O(n \log n) time when the input points lie in the d-dimensional Euclidean space R^d, where d is a constant. We also prove that this problem cannot be approximated within a factor of 1.8-\epsilon unless P = \NP even if the input points are points in the Euclidean plane R^2.

Author

Ene, Alina; Har-Peled, Sariel; Raichel, Benjamin

Published

2013

Language

EN