Random minimal directed spanning trees and Dickman-type distributions
By Mathew D. Penrose, A. Wade. Advances in Applied Probability, 2004
64 citations recorded by the source corpus.
In Bhatt and Roy's minimal directed spanning tree construction for n random points in the unit square, all edges must be in a south-westerly direction and there must be a directed path from each vertex to the root placed at the origin. We identify the limiting distributions (for large n) for the total length of rooted edges, and also for the maximal length of all edges in the tree. These limit distributions have been seen previously in analysis of the Poisson-Dirichlet distribution and elsewhere; they are expressed in terms of Dickman's function, and their properties are discussed in some detail.
Subfields: Applied Mathematics, Artificial Intelligence, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/958e3327c8ca1e9db69999c83665605bf7c3c366
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In Applied Mathematics
In Artificial Intelligence
In Mathematical Physics
Citations in the corpus
- The Radial Spanning Tree of a Poisson Point Process (2007, methodology): “ in the unit square. In this paper we define a new model of rooted tree generated over a point set, the radial spanning tree (RST). This tree holds similarities with the minimal directed spanning tree [6, 21, 22] and the Poisson forest (as defined in [12, 13]). The mathematical analysis of the RST is ”