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...

This paper presents a novel reconstruction algorithm for binary tomography based on the movement of particles. Particle Aggregate Reconstruction Technique (PART) supposes that pixel values are particles, and that the particles can diffuse through the image, sticking together in regions of uniform pixel value known as aggregates. The algorithm is tested on four phantoms of varying sizes and numb...

This paper proposes a new family of multiplier-less discrete cosine and sine transforms called the SOPOT DCTs and DSTs. The fast algorithm of Wang [lo] is used to parameterize all the DCTs and DSTs in terms of certain (2x2) matrices, which are then converted to SOPOT representation using a method previously proposed by the authors [7]. The forward and inverse transforms can be implemented with ...

Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discret...

We present an interactive multi-criteria procedure that uses user defined tradeoff-cutting planes to identify promising feasible solution search space. New solutions in the promising feasible solution search space are constructed using combination of scatter and random search. The procedure of identifying tradeoff-cutting planes and scatter search continues for either a predetermined fixed numb...

We study the number of records in a random binary search tree on n randomly labelled vertices. Equivalently the number of random cuttings required to eliminate a random binary search tree can be studied. After normalization the distribution is shown to be asymptotically 1-stable.

For the random binary search tree with n nodes inserted the number of ancestors of the elements with ranks k and `, 1 ≤ k < ` ≤ n, as well as the path distance between these elements in the tree are considered. For both quantities central limit theorems for appropriately rescaled versions are derived. For the path distance the condition ` − k → ∞ as n → ∞ is required. We obtain tail bounds and ...

The Wiener index has been studied for simply generated random trees, non-plane unlabeled random trees and a huge subclass of random grid trees containing random binary search trees, random medianof-(2k+ 1) search trees, random m-ary search trees, random quadtrees, random simplex trees, etc. An important class of random grid trees for which the Wiener index was not studied so far are random digi...