K-Centerpoints Conjectures for Pointsets in R^d

Nabil Mustafa (1) , Saurabh Ray (2) , Mudassir Shabbir (3)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 NYU
3 RU - Rutgers, The State University of New Jersey [New Brunswick]

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, and the recently-proven ray-shooting theorem. We define two variants: affine k-centerpoints, and topological k-centerpoints. We prove their equivalence in R^2 , and conjecture that these are in fact equivalent in any dimension.

Mots clés: Centerpoint; data depth; Ray Shooting Depth

Domaines: Informatique

Nabil Mustafa, Saurabh Ray, Mudassir Shabbir. K-Centerpoints Conjectures for Pointsets in R^d. International Journal of Computational Geometry and Applications, 2015, 23 (3), pp.23. ⟨10.1142/S0218195915500107⟩. ⟨hal-01188994⟩