On a set of problems on covering of a bounded set
type: Item
instance of: scholarly article
title: On a set of problems on covering of a bounded set
zbMATH Open document ID: 0684.52007
DOI: 10.1007/BF01953365
published in: Acta Mathematica Hungarica
publication date: 1989-01-01T00:00:00Z
review text: The author describes a constructive approach to the search of admissible coverings of a polyhedron by translates of polyhedra. The domain \(S_ 0\) of the covering is a point set of the Euclidean space \(E^ k\), and \(S_ i\), \(i=1,...,n\), are the covering objects. The main attention is paid to the case when the objects \(S_ i\), \(i=0,...,n\), are polyhedra of the space \(E^ k\). A location of the covering objects when each point of the domain of the covering belongs to at least one object is called an admissible covering. The author can give such coverings for arbitrary polyhedra \(S_ i\). He shows the major stages of solutions of this problem and describes algorithms for auxiliary problems occuring at each stage by referring to the respective literature. A numerical example given at the end of the paper shows the acceptability of the approach given and, on the whole, shows difficulties of its realization.
Mathematics Subject Classification ID: 52C17
zbMATH DE Number: 4120906
zbMATH Keywords: polyhedra in k-dimensional Euclidean space
zbMATH Keywords: covering
author: Sergey Yakovlev
reviewed by: Johannes Böhm
MaRDI profile type: Publication
cites work: Q3316129
description: scientific article; zbMATH DE number 4120906