Limit laws for several quantities in random binary search trees that are related to the local shape of a tree around each node can be obtained very simply by applying central limit theorems for rn-dependent random variables . Examples include : the number of leaves (La ), the number of nodes with k descendants (k fixed), the number of nodes with no left child, the number of nodes with k left de...

2 Binary search trees 2 2.1 Definition of a binary search tree . . . . . . . . . . . . . . . . . . 2 2.2 Profile of a binary search tree . . . . . . . . . . . . . . . . . . . . 3 2.2.1 Level polynomial. BST martingale . . . . . . . . . . . . . 3 2.2.2 Embedding in continuous time. Yule tree . . . . . . . . . . 6 2.2.3 Connection Yule tree binary search tree . . . . . . . . . . 7 2.2.4 Asymptoti...

We apply the Area Decay Law (ADL) straightforwardly to simulate a quark string hadronization and compare the results with the explicit analytic calculations. We show that the usual " inclusive " Monte–Carlo simulations do not correspond to the ADL because of two mistakes: not proper simulation of two–dimensional probability density and lack of an important combinatorial factor in a binary tree ...

This work proposes a trainable system for summarizing news and obtaining an approximate argumentative structure of the source text. To achieve these goals we use several techniques and heuristics, such as detecting the main concepts in the text, connectivity between sentences, occurrence of proper nouns, anaphors, discourse markers and a binary-tree representation (due to the use of an agglomer...

In the book of Knuth (1972) an extensive discussion can be found on some problems concerning rooted trees. Given a prescribed number of end-vertices, one may ask for the binary (or ternary) tree with minimal external path length (i.e. minimal sum of path lengths from the root to end-vertices), or minimal weighted external path length (here the end-vertices have given weights). In the first case...

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...

The purpose of this paper is to settle two conjectures by Flajolet, Gourdon and Martinez ( 1996). We confirm that in a random binary tree on n nodes, the expected number of different subtrees grows indeed as 0 (n/ log n). Secondly, if K is the largest integer such that all possible shapes of subtrees of cardinality less than or equal to K occur in a random binary search tree, then we show that ...

In the state of the art of computer designing interconnection of a huge number of circuit elements in a small enough area possess a challenge for the designers. This is possible if the task is divided into smaller independent modules. This is helpful for concurrent design of the individual modules as well. Interestingly the suitable placement and proper interconnection of these modules became a...

In [5, 6] we introduced three Hopf algebras on planar binary trees related to the renormalization of quantum electrodynamics. One of them, the algebra H, is commutative, and is therefore the ring of coordinate functions of a proalgebraic group G. The other two algebras, H and H , are free non-commutative. Therefore their abelian quotients are the coordinate rings of two proalgebraic groups G an...