article

Diameter partitioning

Author:

David AvisAuthors Info & Claims

Discrete & Computational Geometry, Volume 1, Issue 3

Pages 265 - 276

https://doi.org/10.1007/BF02187699

Published: 01 December 1986 Publication History

Abstract

We discuss the problem of partitioning a set of points into two subsets with certain conditions on the diameters of the subsets and on their cardinalities. For example, we give anO(n2 logn) algorithm to find the smallestt such that the set can be split into two equal cardinality subsets each of which has diameter at mostt. We also give an algorithm that takes two pairs of points (x, y) and (s, t) and decides whether the set can be partitioned into two subsets with the respective pairs of points as diameters.

References

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D. Avis, Non-partitionable point sets,Inform. Proc. Lett.19 (1984), 125---129.

Digital Library

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Cited By

Monma CPaterson MSuri SYao F(2023)Computing euclidean maximum spanning treesAlgorithmica10.1007/BF018403965:1-4(407-419)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/BF01840396
Alsuwaiyel M(2001)A Parallel Algorithm for Partitioning a Point Set to Minimize the Maximum of DiametersJournal of Parallel and Distributed Computing10.1006/jpdc.2000.170661:5(662-666)Online publication date: 1-May-2001
https://dl.acm.org/doi/10.1006/jpdc.2000.1706
Chang MTang CLee RHwang CBrice R(1991)A unified approach for solving bottleneck k-bipartition problemsProceedings of the 19th annual conference on Computer Science10.1145/327164.327202(39-47)Online publication date: 1-Apr-1991
https://dl.acm.org/doi/10.1145/327164.327202
Show More Cited By

Index Terms

Diameter partitioning
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 1, Issue 3

September 1986

89 pages

ISSN:0179-5376

Issue’s Table of Contents

Copyright © Copyright © 1986 Springer-Verlag New York Inc.

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1986

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Cited By

Monma CPaterson MSuri SYao F(2023)Computing euclidean maximum spanning treesAlgorithmica10.1007/BF018403965:1-4(407-419)Online publication date: 22-Mar-2023
https://dl.acm.org/doi/10.1007/BF01840396
Alsuwaiyel M(2001)A Parallel Algorithm for Partitioning a Point Set to Minimize the Maximum of DiametersJournal of Parallel and Distributed Computing10.1006/jpdc.2000.170661:5(662-666)Online publication date: 1-May-2001
https://dl.acm.org/doi/10.1006/jpdc.2000.1706
Chang MTang CLee RHwang CBrice R(1991)A unified approach for solving bottleneck k-bipartition problemsProceedings of the 19th annual conference on Computer Science10.1145/327164.327202(39-47)Online publication date: 1-Apr-1991
https://dl.acm.org/doi/10.1145/327164.327202
Hershberger JSuri SMehlhorn K(1989)Finding tailored partitionsProceedings of the fifth annual symposium on Computational geometry10.1145/73833.73862(255-265)Online publication date: 5-Jun-1989
https://dl.acm.org/doi/10.1145/73833.73862
Jaromczyk JKowaluk MEdelsbrunner H(1988)Skewed projections with an application to line stabbing in R3Proceedings of the fourth annual symposium on Computational geometry10.1145/73393.73430(362-370)Online publication date: 6-Jan-1988
https://dl.acm.org/doi/10.1145/73393.73430
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
Monma CPaterson MSuri SYao FEdelsbrunner H(1988)Computing Euclidean maximum spanning treesProceedings of the fourth annual symposium on Computational geometry10.1145/73393.73418(241-251)Online publication date: 6-Jan-1988
https://dl.acm.org/doi/10.1145/73393.73418
Avis DWenger R(1988)Polyhedral line transversals in spaceDiscrete & Computational Geometry10.1007/BF021879113:3(257-265)Online publication date: 1-Dec-1988
https://dl.acm.org/doi/10.1007/BF02187911
Avis DWenger R(1987)Algorithms for line transversals in spaceProceedings of the third annual symposium on Computational geometry10.1145/41958.41990(300-307)Online publication date: 1-Oct-1987
https://dl.acm.org/doi/10.1145/41958.41990

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