Support vector machine (SVM) with a binary tree architecture is popular since it requires the minimum number of binary SVM to be trained and tested. Many efforts have been made to design the optimal binary tree architecture. However, these methods usually construct a binary tree by a greedy search. They sequentially decompose classes into two groups so that they consider only local optimum at e...

An optimal binary search tree is a binary search tree for which the nodes are arranged on levels such that the tree cost is minimum. For the purpose of a better presentation of optimal binary search trees, we will consider “extended binary search trees”, which have the keys stored at their internal nodes. Suppose “n” keys k1, k2, ... , k n are stored at the internal nodes of a binary search tre...

The paper introduces an operation on a binary tree, called binary tree roll, or roll of a binary tree. Two versions of the binary tree roll, counterclockwise and clockwise, are presented. The operations are mathematically defined and graphically presented. It is explained how the binary tree roll actually coincides with the process of turning the entire tree 90 degrees counterclockwise or clock...

Considering a random binary tree with n labelled leaves, we use a pruning procedure on this tree in order to construct a β( 3 2 , 1 2 )-coalescent process. We also use the continuous analogue of this construction, i.e. a pruning procedure on Aldous’s continuum random tree, to construct a continuous state space process that has the same structure as the β-coalescent process up to some time chang...

We prove that any logarithmic binary tree admits a linear-area straight-line strictly-upward planar grid drawing (in short, strictly-upward drawing), that is, a drawing in which (a) each edge is mapped into a single straight-line segment, (b) each node is placed below its parent, (c) no two edges intersect, and (d) each node is mapped into a point with integer coordinates. Informally, a logarit...

The weighted path length of optimum binary search trees is bounded above by Y'./3i + 2 a. + H where H is the entropy of the frequency distribution, /3i is the total weight of the internal nodes, and aj is the total weight of the leaves. This bound is best possible. A linear time algorithm for constructing nearly optimal trees is described. One of the popular methods for retrieving information b...

The method to deal with the tag collision in RFID system can be directly called “Multiple Access”. According to the ideas of these different anti-collision algorithms, they can be divided into two categories. One is the binary tree algorithm based on deterministic; the other is the statistical-based ALOHA algorithm. Overall, however, there is still room for improvement on anti-collision algorit...

2 Binary search trees 2 2.1 Definition of a binary search tree . . . . . . . . . . . . . . . . . . 2 2.2 Profile. Discrete martingale . . . . . . . . . . . . . . . . . . . . . 3 2.3 Embedding in continuous time. Yule tree . . . . . . . . . . . . . . 4 2.4 Martingale connection Yule tree binary search tree . . . . . . . . 5 2.5 Asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

In this paper we propose a new class of tree machines, called generalized compressed tree machines. Generalized compressed tree machines are obtained from complete binary tree machines by performing certain`con-traction' operations. A generalized compressed tree machine of height h has approximately 25% less number of processors than a complete binary tree of height h. We show that these machin...