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Euclidean minimum spanning trees and bichromatic closest pairs

Euclidean minimum spanning trees and bichromatic closest pairs E u c l i d e a n M i n i m u m S p a n n i n g Trees a n d B i c h r o m a t i c C l o s e s t Pairs* Pankaj K. Agarwal t Department of Computer Science, Duke University,Durham, N C 27706, U S A Herbert Edelsbrunner Department of Computer Science, University of/llinoisat Urbana.Champalgn, Urbana, Illinois61801, U S A Otfried Schwarzkopf E m o Welzl Institut ffirInformatik, Fachbereich MathercaLtik,Frele Urdversit&t Berlin, Arnlmallee 2-6, D-1000 Berlin.J3, West Germany Abstract We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in E a in time O ( ~ ( A r, ~r)log d N), where 7~(n, m) is ~he time required to compute a bichromatic closest pair among n red and rn blue points in E a. I f Ta(N, N ) = 12(Nl+'), for some fized > O, then the running time improves to O(7~( N, N ) ). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in ezpected time O((nrn log n log rn) '/3 + m http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Euclidean minimum spanning trees and bichromatic closest pairs

Association for Computing Machinery — May 1, 1990

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Datasource
Association for Computing Machinery
Copyright
Copyright © 1990 by ACM Inc.
ISBN
0-89791-362-0
doi
10.1145/98524.98567
Publisher site
See Article on Publisher Site

Abstract

E u c l i d e a n M i n i m u m S p a n n i n g Trees a n d B i c h r o m a t i c C l o s e s t Pairs* Pankaj K. Agarwal t Department of Computer Science, Duke University,Durham, N C 27706, U S A Herbert Edelsbrunner Department of Computer Science, University of/llinoisat Urbana.Champalgn, Urbana, Illinois61801, U S A Otfried Schwarzkopf E m o Welzl Institut ffirInformatik, Fachbereich MathercaLtik,Frele Urdversit&t Berlin, Arnlmallee 2-6, D-1000 Berlin.J3, West Germany Abstract We present an algorithm to compute a Euclidean minimum spanning tree of a given set S of n points in E a in time O ( ~ ( A r, ~r)log d N), where 7~(n, m) is ~he time required to compute a bichromatic closest pair among n red and rn blue points in E a. I f Ta(N, N ) = 12(Nl+'), for some fized > O, then the running time improves to O(7~( N, N ) ). Furthermore, we describe a randomized algorithm to compute a bichromatic closest pair in ezpected time O((nrn log n log rn) '/3 + m

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