N. J. A. Sloane: Papers on Sphere Packings, Lattices and Quadratic Forms (see also Spherical Codes and Designs)
http://www2.research.att.com/~njas/doc/sp.html
"In combinatorics and computer science, covering problems are computational problems that ask whether a certain combinatorial structure 'covers' another, or how large the structure has to be to do that. Covering problems are minimization problems and usually linear programs, whose dual problems are called packing problems.
The most prominent examples of covering problems are the set cover problem, which is equivalent to the hitting set problem, and its special cases, the vertex cover problem and the edge cover problem."
http://en.wikipedia.org/wiki/Covering_problem
"Packing problems are a class of optimization problems in mathematics which involve attempting to pack objects together (often inside a container), as densely as possible. Many of these problems can be related to real life packaging, storage and transportation issues. Each packing problem has a dual covering problem, which asks how many of the same objects are required to completely cover every region of the container, where objects are allowed to overlap.
In a packing problem, you are given:
'containers' (usually a single two- or three-dimensional convex region, or an infinite space)
'goods' (usually a single type of shape), some or all of which must be packed into this container
Usually the packing must be without overlaps between goods and other goods or the container walls. The aim is to find the configuration with the maximal density. In some variants the overlapping (of goods with each other and/or with the boundary of the container) is allowed but should be minimized."
http://en.wikipedia.org/wiki/Packing_problem
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