Packing and Covering by Translates of Certain Nonconvex Bodies
نویسندگان
چکیده
منابع مشابه
Packing and Covering by Translates of Certain Nonconvex Bodies
We develop techniques for determining the packing and covering constants for star bodies composed of cubes. In the theory of convex sets problems of tiling, packing, and covering by translates of a given set have a long history, with the main focus on the packing and covering by spheres. Only in a few cases is the densest packing or sparsest covering known, even in the case of the sphere, excep...
متن کاملPacking and covering constants for certain families of trees. I
In an earlier paper we considered the problem of determining the packing and covering constants for families of trees whose generating function^ satisfied a relation y = x(y) for some power series itiy. In the present paper we consider the problem for some families of trees whose generating functions satisfy a more complicated relation.
متن کاملOn covering by translates of a set
In this paper we study the minimal number τ(S,G) of translates of an arbitrary subset S of a group G needed to cover the group, and related notions of the efficiency of such coverings. We focus mainly on finite subsets in discrete groups, reviewing the classical results in this area, and generalizing them to a much broader context. For example, we show that while the worst-case efficiency when ...
متن کاملPacking and covering a tree by subtrees
(P0) Max Z {c(V)x(T): TEo~} subject to ~ ' { x ( T ) : T)v} _-< 1 (vEV), x(r)~{0, 1} (rc~), where c(T) is a weight function on -~. It is known that this problem can be solved by a polynomial-time algorithm as the intersection graph of o~ is triangulated [3] and the maximum weighted stable set problem on a triangulated graph can be solved efficiently [2], see also [4]. In this paper we consider ...
متن کامل2 Packing and Covering
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 arrange...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.2307/2042678