Vector packing in finite dimensional vector spaces |
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Authors: | Michael H. Moore |
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Affiliation: | University of Florida Gainesville, Florida, USA |
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Abstract: | Let m be an integer ? 2. The effect of crowding m unit vectors x1,…,xm into the real Euclidean space Rn of n dimensions is investigated. In particular, several upper bounds for the quantity mini≠j∥xi ? xj∥ are obtained. These are simpler than any previously known and, at least in some cases, almost as sharp. The results have application to the so-called maximum-dispersal (or “misanthrope”) problem, an open problem recently popularized by Klee. |
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