Affiliation:
1. Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124, USA
Abstract
Given an n-point set, the problems of enumerating the k closest pairs and selecting the k-th smallest distance are revisited. For the enumeration problem, we give simpler randomized and deterministic algorithms with O(n log n+k) running time in any fixed-dimensional Euclidean space. For the selection problem, we give a randomized algorithm with running time O(n log n+n2/3k1/3 log 5/3n) in the Euclidean plane. We also describe output-sensitive results for halfspace range counting that are of use in more general distance selection problems. None of our algorithms requires parametric search.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science
Cited by
11 articles.
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