Generally the result data from DNA chip experiments have lots of gene expression information. Scientists want to get perspective insight or want to find intuitive fact from that data. Hierarchical clustering is the most widely used method for analysis of gene expression data. In this paper, we address leaf-ordering, which is a post-processing for the dendrograms – a sort of edge-weighted binary...

The problem this paper focuses on is the unsupervised clustering of a data-set. The dataset is given by the matrix [ ] N p N x x x M × R ∈ = ,..., , 2 1 , where each column of M, p i x R ∈ , is a single data-point. This is one of the more basic and common problems in fields like pattern analysis, data mining, document retrieval, image segmentation, decision making, etc. ([12, 13]). The specific...

BSP trees and KD trees are fundamental data structures for collision detection in walkthrough environments. A basic issue in the construction of these hierarchical data structures is the choice of cutting planes. Rather than base these choices solely on the properties of the scene, we propose using information about how the tree is used in order to determine its structure. We demonstrate how th...

abstract: background: depending on the importance of a good performance appraisal system to achieve organizational strategies, balanced scorecard technique provides a comprehensive foundation for interpreting and translating organization’s vision and strategy in a set of performance measures by regarding an overall view of organization in four perspectives included customer, internal processes,...

A phylogenetic tree on a label set L is a tree which exactly ILl leaves (vert.ices of degree one), no vertices of degree two, and each leaf labeled with a distinct element from L. A binary phylogenetic tree is a phylogenetic tree in which every non-leaf has degree three. Phylogenetic trees get their name because they are often appropriate models for evolutionary history. However, for simplicity...

Invented in the 70’s, the Suffix Tree (ST) is a data structure that indexes all substrings of a text in linear space. Although more space demanding than other indexes, the ST remains an inspiring index likely because it represents substrings in a hierarchical tree structure. Along time, STs have acquired a central position in text algorithmics with myriad of algorithms and applications to for i...

If we insert a set of n items into a binary search tree using TREE-INSERT, the resulting tree may be horribly unbalanced. As we saw in class, however, we expect randomly built binary search trees to be balanced. (Precisely, a randomly built binary search tree has expected height O(lg n).) Therefore, if we want to build an expected balanced tree for a fixed set of items, we could randomly permut...

In this note, we give a parity reversing involution on colored binary trees which leads to a combinatorial interpretation of Formula (1.2). We make a simple variation of the bijection between colored ternary trees and binary trees proposed by Sun [2] and find a correspondence between certain class of binary trees and the set of colored 5-ary trees. The generalization of the parity reversing inv...

In linguistics, it is quite common to use tree diagrams for immediate constituent analysis of sentences. Traditionally, these trees are binary and twodimensional. However, phenomena such as coordination and right node raising, have led to the view that a simple hierarchical approach of sentences is inadequate: some linguistic phenomena rather seem to involve non-subordination and multiple depen...

The problem of performing a search procedure when some of the answers to queries may be erroneous has been recently investigated by many authors (see [3,4, 2, 11). One of the main questions in this domain was stated by S. M. Ulam [S]: what is the minimal number of yes-no queries sufficient to find an unknown object in an n-element set if at most one answer may be erroneous? This problem was fir...