Near-Optimal $\varepsilon$-Kernel Construction and Related Problems
Sunil Arya,
Guilherme D. da Fonseca,
David M. Mount
Abstract:The computation of (i) ε-kernels, (ii) approximate diameter, and (iii) approximate bichromatic closest pair are fundamental problems in geometric approximation. In this paper, we describe new algorithms that offer significant improvements to their running times. In each case the input is a set of n points in R d for a constant dimension d ≥ 3 and an approximation parameter ε > 0. We reduce the respective running times), and (iii) from O(n/ε d/3 ) to O(n/ε d/4+α ), for an arbitrarily small constant α > 0. Resul… Show more
Set email alert for when this publication receives citations?
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.