Asymptotics for Euclidean minimal spanning trees on random points
✍ Scribed by David Aldous; J. Michael Steele
- Publisher
- Springer
- Year
- 1992
- Tongue
- English
- Weight
- 612 KB
- Volume
- 92
- Category
- Article
- ISSN
- 1432-2064
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📜 SIMILAR VOLUMES
A general formulation is presented for continuum scaling limits of stochastic spanning trees. A spanning tree is expressed in this limit through a consistent collection of subtrees, which includes a tree for every finite set of endpoints in ޒ d . Tightness of the distribution, as ␦ ª 0, is establi
The N-cube is a graph with 2 N vertices and N 2 Ny1 edges. Suppose indepen- dent uniform random edge weights are assigned and let T be the spanning tree of minimal Ž . y 1 N ϱ y3 total weight. Then the weight of T is asymptotic to N 2 Ý i as N ª ϱ. Asymp-is1 totics are also given for the local stru
Steele (1988 , Ann. Probab. 16, 1767-1787) has proved that the total length of several combinatorial optimization problems in R p involving trees with n nodes and -power-weighted edges is asymptotically c(p; )n (p-)=p , where 0 ¡ 6p. In this paper we obtain bounds for these constants and give esti
Penrose has given asymptotic results for the distribution of the longest edge of the minimal spanning tree and nearest neighbour graph for sets of multivariate uniformly or normally distributed points. We investigate the applicability of these results to samples of up to 100 points, in up to 10 dime