Packing and Covering

Authored by: Gábor Fejes Tóth

Discrete and Computational Geometry

Print publication date:  April  2004
Online publication date:  April  2004

Print ISBN: 9781584883012
eBook ISBN: 9781420035315
Adobe ISBN:

10.1201/9781420035315.ch2

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Abstract

The basic problems in the classical theory of packings and coverings, the development of which was strongly influenced by the geometry of numbers and by crystallography, are the determination of the densest packing and the thinnest covering with congruent copies of a given body K. Roughly speaking, the density of an arrangement is the ratio between the total volume of the members of the arrangement and the volume of the whole space. In Section 2.1 we define this notion rigorously and give an account of the known density bounds.

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