Discrete & Computational Geometry

, Volume 12, Issue 3, pp 291–312

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

Authors

  • S. Jadhav
    • Department of Computer ScienceIndian Institute of Technology
  • A. Mukhopadhyay
    • Department of Computer ScienceIndian Institute of Technology
Article

DOI: 10.1007/BF02574382

Cite this article as:
Jadhav, S. & Mukhopadhyay, A. Discrete Comput Geom (1994) 12: 291. doi:10.1007/BF02574382

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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Copyright information

© Springer-Verlag New York Inc. 1994