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On the limit of multiple packings (1974)

Witsenhausen, H. S.

Springer

Mathematical programming 6 (1974), S. 110-113

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ISSN: 1436-4646

Source: Springer Online Journal Archives 1860-2000

Topics: Computer Science , Mathematics

Notes: Abstract For a collection of subsets of a setS, letn k be the maximal number of sets from such that no point ofS belongs to more thank of them. Then the limitδ of the sequencen k /k is related to the valuev of the game in which the minimizer selects a setα in , the maximizer a pointx inS, and the payoff isϰ α (x), byδ≤v −1≤inf v δ v . Herev is any finite subset ofS and δ v the corresponding limit. Analogous results hold for covering. The bounds obtained in this way forn k and in particularn 1 reflect the influence of the boundary ofS when, for instance,S is a convex body to be packed with congruent copies of another body. In some cases, the bounds are sharp.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01580226

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