A Conjecture on Different Central Parts of Binary Trees

Some results on Hu's conjecture concerning binary trees

Given n weights, w I, w2, . . . , w,, such that 0 G w 1 G w2 S. . . s w ,, we examine a property of permutation #, where 7~* = (w,, w,,, w2, w,,_r, . . .), concerning alphabetical binary trees. For each permutation ‘CT of these n weights, there is an optimal alphabetical binary tree corresponding to ‘TT, we denote it’s cost by V(m). There is also an optimal almost uniform alphabetical binary tr...

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...

On a Conjecture about Binary Strings Distribution

It is a difficult challenge to find Boolean functions used in stream ciphers achieving all of the necessary criteria and the research of such functions has taken a significant delay with respect to cryptanalyses. A lot of attacks has led to design criteria for these functions; mainly: balancedness, a high algebraic degree, a high nonlinearity, a good behavior against Fast Algebraic Attacks and ...

On Random Binary Trees

A widely used class of binary trees is studied in order to provide information useful in evaluating algorithms based on this storage structure. A closed form counting formula for the number of binary trees with n nodes and height k is developed and restated as a recursion more useful computationally . A generating function for the number of nodes given height is developed and used to find the a...

On Robson's Convergence and Boundedness Conjecture Concering the Height of Binary Search Trees