منابع مشابه
On Weighted Heights of Random Trees
Consider the family tree T of a branching process starting from a single progenitor and conditioned to have v=v(T) edges (total progeny). To each e d g e ( e ) we associate a weight W(e). The weights are i.i.d, random variables and independent of T. The weighted height of a self-avoiding path in T starting at the root is the sum of the weights associated with the path. We are interested in the ...
متن کاملRandom Trees, Heights, and Large Deviations
Random trees are of prime importance for studying the average case behavior of algorithms and data structures. The canonical examples are Hoare’s quicksort algorithm and the binary search tree. The most natural parameter to study is the average running time of the algorithm, and the average time for answering a query in a data structure. This does not provide sufficient information to properly ...
متن کاملOn Heights of Monotonically Labelled Binary Trees
A monotonically labelled binary tree is a binary tree with integer labels attached to the internal nodes in such a way that the labels along any path from the root are nondecreasing. If there is only one label, we are dealing with ordinary binary trees. Prodinger and Urbanek [6] introduced a variety of families of monotonically labelled trees and obtained enumerative results about many of them....
متن کاملOn weighted depths in random binary search trees
Following the model introduced by Aguech, Lasmar and Mahmoud [Probab. Engrg. Inform. Sci. 21 (2007) 133–141], the weighted depth of a node in a labelled rooted tree is the sum of all labels on the path connecting the node to the root. We analyze weighted depths of nodes with given labels, the last inserted node, nodes ordered as visited by the depth first search process, the weighted path lengt...
متن کاملNon-Uniform Random Spanning Trees on Weighted Graphs
We study random walks on undirected graphs with weighted edges. Our main result shows that any spanning tree deened by the edges corresponding to a rst visit of a vertex, appears with a probability proportional to its weight, which is the product of the weights of its edges. This provides an algorithm for generating non uniform random spanning trees in a weighted graph. The technique used here ...
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 1991
ISSN: 0894-9840,1572-9230
DOI: 10.1007/bf01047004