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...

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...

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...

A chordal graph is the intersection graph of a family of subtrees of a tree, or, equivalently, it is the (edge-)intersection graph of leaf-generated subtrees of a full binary tree. In this paper, a generalization of chordal graphs from this viewpoint is studied: a graph G=(V; E) is representable if there is a family of subtrees {Sv}v∈V of a binary tree, such that uv ∈ E if and only if |Su ∩ Sv|...

In this paper we present a polynomial time algorithm for finding the shortest sequence of rotations that converts one binary tree into another when both binary trees are of a restricted form. The initial tree must be a degenerate tree, where every node has exactly one child, and the destination binary tree must also be degenerate, of a more restricted nature. Previous work on rotation distance ...

In this paper an "Augmented Binary Tree" architecture is proposed with a view to provide faulttolerance. This architecture is an augmentation of an n-level full binary tree with n redundant nodes and 2+3n-6 redundant links. The AB-tree can be configured into a full binary tree even when one node is faulty at each level. While functionally equivalent to the RAE-tree [13], the proposed AB-tree ha...

Abstract— For multi-class classification with Support Vector Machines (SVMs) a binary decision tree architecture is proposed for computational efficiency. The proposed SVMbased binary tree takes advantage of both the efficient computation of the tree architecture and the high classification accuracy of SVMs. A modified Self-Organizing Map (SOM), KSOM (Kernel-based SOM), is introduced to convert...

This article discusses how to use queue to make non-recursion algorithm of binary link tree. As for a general binary tree, if we adopt sequence storage, firstly we should extend it first into a complete binary tree, secondly we store it to a temporary queue according to the sequence of up-down and left-right. On the basis of the properties of the complete binary tree and the queue, if we can co...

A binary-tree algorithm, Bin(n), proceeds level-bylevel from the leaves of a 2-leaf balanced binary tree to its root. This paper deals with running binary-tree algorithms on multiple bus networks (MBNs) in which processors communicate via buses. Every “binary-tree MBN” has a degree (maximum number of buses connected to a processor) of at least 2. There exists a degree-2 MBN [15] for Bin(n) that...