Shapes of Binary Trees
نویسنده
چکیده
max 0≤≤1 ̄̄̄̄ + − 2 min ≤≤ ̄̄̄̄ if =∞ We examined k k earlier [2]; h i is a less familiar random variable but nevertheless important in the study of trees. Note that h i is not a norm since, for any constant , hi = 0 even if 6= 0. Let be an ordered (strongly) binary tree with = 2+1 vertices. The distance between two vertices of is the number of edges in the shortest path connecting them. The height of a vertex is the number of edges in the shortest path connecting the vertex and the root. TheWiener index 1( ) is the sum of all ¡ 2 ¢ distances between pairs of distinct vertices of , and the diameter ∞( ) is the maximum such distance. If ( ) denotes the distance between vertices and , then
منابع مشابه
A New Heuristic Algorithm for Drawing Binary Trees within Arbitrary Polygons Based on Center of Gravity
Graphs have enormous usage in software engineering, network and electrical engineering. In fact graphs drawing is a geometrically representation of information. Among graphs, trees are concentrated because of their ability in hierarchical extension as well as processing VLSI circuit. Many algorithms have been proposed for drawing binary trees within polygons. However these algorithms generate b...
متن کاملProfile and Height of Random Binary Search Trees
The purpose of this article is to survey recent results on distributional properties of random binary search trees. In particular we consider the profile and the height.
متن کاملThe most parsimonious tree for random data.
Applying a method to reconstruct a phylogenetic tree from random data provides a way to detect whether that method has an inherent bias towards certain tree 'shapes'. For maximum parsimony, applied to a sequence of random 2-state data, each possible binary phylogenetic tree has exactly the same distribution for its parsimony score. Despite this pleasing and slightly surprising symmetry, some bi...
متن کاملP´olya Urn Models and Connections to Random Trees: A Review
This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...
متن کاملOn the Balance of Unrooted Trees
We solve a class of optimization problems for (phylogenetic) X-trees or their shapes. These problems have recently appeared in different contexts, e.g. in the context of the impact of tree shapes on the size of TBR neighborhoods, but so far these problems have not been characterized and solved in a systematic way. In this work we generalize the concept and also present several applications. Mor...
متن کامل