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Computing Euclidean maximum spanning trees

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F. YaoAuthors Info & Claims

SCG '88: Proceedings of the fourth annual symposium on Computational geometry

Pages 241 - 251

https://doi.org/10.1145/73393.73418

Published: 06 January 1988 Publication History

Abstract

An algorithm is presented for finding a maximum-weight spanning tree of a set of n points in the Euclidean plane, where the weight of an edge (pi, pj) equals the Euclidean distance between the points pi and pj. The algorithm runs in time Ο (n logn) and requires Ο (n) space. If the points are vertices of a convex polygon (given in order along the boundary), then our algorithm requires only a linear amount of time and space. These bounds are the best possible in the algebraic computation-tree model. We also establish various properties of maximum spanning trees that can be exploited to solve other geometric problems.

References

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T. Asano, B.K. Bhattacharya, J.M. Keil and F.F. Yao, Clustering algorithms based on minimum and maximum spanning trees, these proceedings.

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Cited By

Katoh NIwano K(2006)Efficient algorithms for minimum range cut problemsNetworks10.1002/net.323024070524:7(395-407)Online publication date: 11-Oct-2006
https://doi.org/10.1002/net.3230240705
Seidel R(2005)The nature and meaning of perturbations in geometric computingSTACS 9410.1007/3-540-57785-8_127(1-17)Online publication date: 31-May-2005
https://doi.org/10.1007/3-540-57785-8_127
Asano T(2000)Effective Use of Geometric Properties for ClusteringDiscrete and Computational Geometry10.1007/978-3-540-46515-7_3(30-46)Online publication date: 2000
https://doi.org/10.1007/978-3-540-46515-7_3
Show More Cited By

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Euclidean minimum spanning trees and bichromatic closest pairs

We present an algorithm to compute a Euclidean minimum spanning tree of a given setS ofN points inEd in timeO(Fd(N,N) logdN), whereFd(n,m) is the time required to compute a bichromatic closest pair amongn red andm green points inEd. IfFd(N,N)=Ω(N1+ ), ...
Computing euclidean maximum spanning trees
Abstract
An algorithm is presented for finding a maximum-weight spanning tree of a set ofn points in the Euclidean plane, where the weight of an edge (p_i,p_j) equals the Euclidean distance between the pointsp_i andp_j. The algorithm runs inO(n logh) time and ...
Euclidean minimum spanning trees and bichromatic closest pairs

We present an algorithm to compute a Euclidean minimum spanning tree of a given setS ofN points inEd in timeO(Fd(N,N) logdN), whereFd(n,m) is the time required to compute a bichromatic closest pair amongn red andm green points inEd. IfFd(N,N)=Ω(N1+ ), ...

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cover image ACM Conferences

SCG '88: Proceedings of the fourth annual symposium on Computational geometry

January 1988

403 pages

ISBN:0897912705

DOI:10.1145/73393

Chairman:
H. Edelsbrunner
Univ. of Illinois, Urbana-Champaign

Copyright © 1988 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 January 1988

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CG88: Symposium on Computational Geometery

June 6 - 8, 1988

Illinois, Urbana-Champaign, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Katoh NIwano K(2006)Efficient algorithms for minimum range cut problemsNetworks10.1002/net.323024070524:7(395-407)Online publication date: 11-Oct-2006
https://doi.org/10.1002/net.3230240705
Seidel R(2005)The nature and meaning of perturbations in geometric computingSTACS 9410.1007/3-540-57785-8_127(1-17)Online publication date: 31-May-2005
https://doi.org/10.1007/3-540-57785-8_127
Asano T(2000)Effective Use of Geometric Properties for ClusteringDiscrete and Computational Geometry10.1007/978-3-540-46515-7_3(30-46)Online publication date: 2000
https://doi.org/10.1007/978-3-540-46515-7_3
Katoh NTokuyama TIwano K(1995)On minimum and maximum spanning trees of linearly moving pointsDiscrete & Computational Geometry10.1007/BF0257403513:2(161-176)Online publication date: 1-Mar-1995
https://doi.org/10.1007/BF02574035
Eppstein DSleator D(1994)Average case analysis of dynamic geometric optimizationProceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms10.5555/314464.314481(77-86)Online publication date: 23-Jan-1994
https://dl.acm.org/doi/10.5555/314464.314481
Katoh NTokuyama TIwano K(1992)On minimum and maximum spanning trees of linearly moving pointsProceedings of the 33rd Annual Symposium on Foundations of Computer Science10.1109/SFCS.1992.267750(396-405)Online publication date: 24-Oct-1992
https://dl.acm.org/doi/10.1109/SFCS.1992.267750
Smith W(1992)How to find Steiner minimal trees in euclideand-spaceAlgorithmica10.1007/BF017587567:1-6(137-177)Online publication date: Jun-1992
https://doi.org/10.1007/BF01758756
Katoh NIwano K(1991)Efficient algorithms for the minimum range cut problemsAlgorithms and Data Structures10.1007/BFb0028252(80-91)Online publication date: 1991
https://doi.org/10.1007/BFb0028252
Asano TBhattacharya BKeil MYao FEdelsbrunner H(1988)Clustering algorithms based on minimum and maximum spanning treesProceedings of the fourth annual symposium on Computational geometry10.1145/73393.73419(252-257)Online publication date: 6-Jan-1988
https://dl.acm.org/doi/10.1145/73393.73419

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