Classes of discrete convexity properties
type: Item
instance of: scholarly article
title: Classes of discrete convexity properties
zbMATH Open document ID: 1069.52013
author: Gabriela Cristescu
author: Liana Lupşa
published in: Discrete \& Computational Geometry
publication date: 2004-12-16T00:00:00Z
review text: In the general first-level classification of the convexity properties for sets [\textit{G. Cristescu} and \textit{L. Lupsa}, Bul. Stünt. Univ. Baia Mare, Ser. B 18, 23--30 (2002; Zbl 1036.52001)], discrete convexities appear in more classes. A second-level classification identifies more subclasses containing discrete convexity properties, which appear as approximations either of classical convexity or of fuzzy convexity. In this paper the authors prove that all these convexity concepts are defined by segmential methods. The subclasses containing the convexity properties that have discrete particular cases are also presented. Axiomatic convexities that allow the construction of various discrete models are not considered in this paper. The authors prefer to make a unifying systematic discussion of the discrete convexities that appear in various applications in integer programming or in pattern recognition for instance.
reviewed by: Hans-Dietrich Hecker
Mathematics Subject Classification ID: 52A99
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 68U05
Mathematics Subject Classification ID: 68T10
zbMATH DE Number: 2123199
zbMATH Keywords: convex sets
zbMATH Keywords: convexity properties
MaRDI profile type: Publication
full work available at URL: s00454-003-2877-x
OpenAlex ID: W1981809986
DOI: 10.1007/S00454-003-2877-X
description: scientific article; zbMATH DE number 2123199