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On strong centerpoints

Ashok, Pradeesha and Govindarajan, Sathish (2015) On strong centerpoints. In: INFORMATION PROCESSING LETTERS, 115 (3). pp. 431-434.

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Official URL: http://dx.doi.org/ 10.1016/j.ipl.2014.11.004

Abstract

Let P be a set of n points in R-d and F be a family of geometric objects. We call a point x is an element of P a strong centerpoint of P w.r.t..F if x is contained in all F is an element of F that contains more than cn points of P, where c is a fixed constant. A strong centerpoint does not exist even when F is the family of halfspaces in the plane. We prove the existence of strong centerpoints with exact constants for convex polytopes defined by a fixed set of orientations. We also prove the existence of strong centerpoints for abstract set systems with bounded intersection. (C) 2014 Elsevier B.V. All rights reserved.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS
Keywords: Discrete geometry; Centerpoint; Strong centerpoint; Convex polytopes; Hyperplanes
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 19 Mar 2015 11:35
Last Modified: 19 Mar 2015 11:35
URI: http://eprints.iisc.ac.in/id/eprint/51023

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