article

Computing a centerpoint of a finite planar set of points in linear time

Authors:

S. Jadhav,

A. MukhopadhyayAuthors Info & Claims

Discrete & Computational Geometry, Volume 12, Issue 3

Pages 291 - 312

Published: 01 December 1994 Publication History

Abstract

The notion of a centerpoint of a finite set of points in two and higher dimensions is a generalization of the concept of the median of a set of reals. In this paper we present a linear-time algorithm for computing a centerpoint of a set ofn points in the plane, which is optimal compared with theO(n log3n) complexity of the previously best-known algorithm. We use suitable modifications of the hamsandwich cut algorithm in [Me2] and the prune-and-search technique of Megiddo [Me1] to achieve this improvement.

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H. Edelsbrunner. Algorithms in Combinatorial Geometry. Springer-Verlag, New York, 1987.

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S. Jadhav and A. Mukhopadhyay. Designing optimal geometric algorithms using partial sorting networks. Technical Report TRCS-93-165, Indian Institute of Technology, Kanpur, 1993. Accepted in the Third National Seminar on Theoretical Computer Science, 1993, Kharagpur, India.

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J. Matoušek. Approximations and optimal geometric divide-and-conquer. Proc. 23rd Annual ACM Symposium on Theory of Computing, pages 505-511, 1991.

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N. Megiddo. Linear-time algorithms for linear programming in R<sup>3</sup> and related problems. SIAM J. Comput., 12(4):759-776, 1983.

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N. Megiddo. Partitioning with two lines in the plane. J. Algorithms, 3:430-433, 1985.

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cover image Discrete & Computational Geometry

Discrete & Computational Geometry Volume 12, Issue 3

September 1994

142 pages

ISSN:0179-5376

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 December 1994

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Haxen MRaeburn MAfshani PKarras PDemartini GZuccon GCulpepper JHuang ZTong H(2021)Centerpoint Query AuthenticationProceedings of the 30th ACM International Conference on Information & Knowledge Management10.1145/3459637.3482072(3083-3087)Online publication date: 26-Oct-2021
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Abbas WShabbir MLi JKoutsoukos X(2020)Interplay Between Resilience and Accuracy in Resilient Vector Consensus in Multi-Agent Networks2020 59th IEEE Conference on Decision and Control (CDC)10.1109/CDC42340.2020.9304098(3127-3132)Online publication date: 14-Dec-2020
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Bhattacharya BNandy SRoy S(2016)Space-efficient algorithm for computing a centerpoint of a set of points in R 2Theoretical Computer Science10.1016/j.tcs.2015.11.048615:C(61-70)Online publication date: 15-Feb-2016
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Mulzer WWerner DDey TWhitesides S(2012)Approximating Tverberg points in linear time for any fixed dimensionProceedings of the twenty-eighth annual symposium on Computational geometry10.1145/2261250.2261294(303-310)Online publication date: 17-Jun-2012
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