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The optimal distribution of a tree in a finite set

โœ Scribed by A.V. Panyukov; B.V. Pel'tsverger

Publisher
Elsevier Science
Year
1988
Weight
219 KB
Volume
28
Category
Article
ISSN
0041-5553

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๐Ÿ“œ SIMILAR VOLUMES

The optimal location of a path or tree i
The optimal location of a path or tree in a tree network
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This article describes methods for finding an optimal location for a path-shaped or tree-shaped facility of a specified size in a tree network. Four optimization criteria are examined: minimizing distancesum, minimizing eccentricity, maximizing distancesum, and maximizing eccentricity.

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Let n k denote the number of times the kth largest distance occurs among a set S of n points. We show that if S is the set of vertices of a convex polygone in the euclidean plane, then n1+2n2~3n and n2<~n +n 1. Together with the well-known inequality n~<~n and the trivial inequalities n~>~O and n2>~