K-Centerpoints Conjectures for Pointsets in Rd

Nabil H. Mustafa; Saurabh Ray; Mudassir Shabbir

doi:10.1142/S0218195915500107

K-Centerpoints Conjectures for Pointsets in R^d

Nabil H. Mustafa, Saurabh Ray, Mudassir Shabbir

Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we introduce the notion of k-centerpoints for any set P of n points in R^d. These unify and generalize previous results such as the classical centerpoint theorem,¹ and the recently-proven ray-shooting theorem.² We define two variants: affine k-centerpoints, and topological k-centerpoints. We prove their equivalence in R², and conjecture that these are in fact equivalent in any dimension. We present the first non-trivial bounds for these problems in R^d, as well as present several conjectures related to them.

Original language	English (US)
Pages (from-to)	163-185
Number of pages	23
Journal	International Journal of Computational Geometry and Applications
Volume	25
Issue number	3
DOIs	https://doi.org/10.1142/S0218195915500107
State	Published - Sep 1 2015

Keywords

Centerpoint
data depth
ray shooting depth

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Computational Theory and Mathematics
Computational Mathematics
Applied Mathematics

Access to Document

10.1142/S0218195915500107

Cite this

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