Combinatorial problems on the illumination of convex bodies
type: Item
instance of: scholarly article
title: Combinatorial problems on the illumination of convex bodies
zbMATH Open document ID: 0937.52006
author: Horst Martini
author: Valeriu Soltan
published in: Aequationes Mathematicae
publication date: 2000-06-07T00:00:00Z
review text: This is a comprehensive survey article on the well known Hadwiger's covering problem and on miscellaneous variants of the equivalent illumination problem. In particular, the most interesting related open questions and conjectures are recalled. The variety of subjects can be immediately seen from the titles of the sections: Gohberg-Marcus-Hadwiger problem, Generalizations for unbounded convex sets, Illumination of special convex bodies, Visibility of a convex body, Inner illumination of a convex body, Primitive illuminating systems for a convex body, Illumination and visibility of a family of convex bodies, Clouds, Miscellaneous results. The reader may compare the present survey with four other extensive surveys about Hadwiger's and illumination problems published in the decade 1990-1999: \textit{K. Bezdek} [New Trends in Discrete and Computational Geometry, Springer, 199-233 (1993; Zbl 0798.52004)], \textit{V. Boltyanskij} and \textit{I. Gohberg} [Nieuw Arch. Wisk. 13, 1-26 (1995; Zbl 0896.52023)], Chapter VI of the book \textit{V. Boltyanskij}, \textit{H. Martini}, and \textit{P. S. Soltan} [Excursions into Combinatorial Geometry, Springer (1997; Zbl 0877.52001)], and \textit{L. Szabó} [Bolyai Soc. Math. Stud. 6, 207-221 (1997; Zbl 0886.52005)].
reviewed by: Marek Lassak
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52-02
zbMATH DE Number: 1320493
zbMATH Keywords: cloud
zbMATH Keywords: shadow-boundary
zbMATH Keywords: survey
zbMATH Keywords: Hadwiger's covering problem
zbMATH Keywords: illumination
MaRDI profile type: Publication
full work available at URL: s000100050074
OpenAlex ID: W2049798553
DOI: 10.1007/S000100050074
description: scientific article; zbMATH DE number 1320493