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Entropy and set covering

✍ Scribed by L.P. Lefkovitch


Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
755 KB
Volume
36
Category
Article
ISSN
0020-0255

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We give formulae for determining the number of ways of writing a finite set as the union of a given number of subsets, in such a way that none of the subsets may be omitted. In particular, we consider the case in which the elements of the set are identical.

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The weighted set covering problem, restricted to the class of r-uniform hypergraphs, is considered. We propose a new approach, based on a recent result of Aharoni, Holzman, and Krivelevich about the ratio of integer and fractional covering numbers in k-colorable r-uniform hypergraphs. This approach,

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In this paper we study a notion of a ΞΊ-covering set in connection with Bernstein sets and other types of nonmeasurability. Our results correspond to those obtained by Muthuvel in [7] and Nowik in [8]. We consider also other types of coverings.