K-Centerpoints Conjectures for Pointsets in Rd

Nabil H. Mustafa, Saurabh Ray, Mudassir Shabbir

Research output: Contribution to journalArticlepeer-review


In this paper, we introduce the notion of k-centerpoints for any set P of n points in Rd. 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 Rd, as well as present several conjectures related to them.

Original languageEnglish (US)
Pages (from-to)163-185
Number of pages23
JournalInternational Journal of Computational Geometry and Applications
Issue number3
StatePublished - Sep 1 2015


  • Centerpoint
  • data depth
  • ray shooting depth

ASJC Scopus subject areas

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


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