Euclidean minimum spanning trees and bichromatic closest pairs
Euclidean minimum spanning trees and bichromatic closest pairs
Agarwal, Pankaj K.; Edelsbrunner, Herbert; Schwarzkopf, Otfried; Welzl, Emo
1990-05-01 00:00:00
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.pnghttp://www.deepdyve.com/lp/association-for-computing-machinery/euclidean-minimum-spanning-trees-and-bichromatic-closest-pairs-rbyOEb0MvJ
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
To get new article updates from a journal on your personalized homepage, please log in first, or sign up for a DeepDyve account if you don’t already have one.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.