Multi-class support vector machines with binary tree architecture (SVM-BTA) have the fastest decision-making speed in the existing multi-class SVMs. But SVM-BTA usually has bad classification capability. According to internal characteristics of feature samples, this paper uses resemblance coefficient method to construct automatically binary tree to incorporate multiple binary SVMs. The multi-cl...

Figure 1: a binary tree Search trees are tree-based data structures that can be used to store and search for items that satisfy a total order. There are many types of search trees designed for a wide variety of purposes. Probably, the most common use is to implement sets and tables (dictionaries, mappings). As shown on right, a binary tree is a tree in which every node in the tree has at most t...

We describe the newly developed wavelet transform of a binary, rooted, labeled tree. The latter corresponds to a hierarchical clustering. We then explore the use of the tree wavelet transform for filtering, i.e. approximating, the tree. Two case studies are pursued in depth. Firstly, we use a multiway tree resulting from the wavelet-based approximation of the binary tree as a means for semi-aut...

In this paper we consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by computing closed formulas for the number of trees avoiding a single binary tree pattern with 4 or fewer leaves and compare these results to analogous work for contiguous tree patterns. Next, we give an explicit generating function that counts binary trees avoiding a single non-con...

We consider several aspects of Wilke’s [T. Wilke, An algebraic characterization of frontier testable tree languages, Theoret. Comput. Sci. 154 (1996) 85–106] tree algebra formalism for representing binary labelled trees and compare it with approaches that represent trees as terms in the traditional way. A convergent term rewriting system yields normal form representations of binary trees and co...

In this paper, we propose novel representation of binary trees, named the balanced ternary-tree representation. We examine flexible division of binary trees in which we can divide a tree at any node rather than just at the root, and introduce the ternary-tree representation for the flexible division. Due to the flexibility of division, for any binary tree, balanced or ill-balanced, there is alw...

The performance of parallel computer systems is increasingly limited by constraints imposed by interconnects and this limitation will inevitably become more serious as capability of each processing node increases. Optics has already proved its worth in telecommunications and more recently in interconnecting computers and computer peripherals. In this paper, we propose an optical hybrid tree net...

Trees are a fundamental structure in algorithmics. In this paper we study the transformation of an arbitrary binary tree S with n vertices into a completely balanced tree T via rotations, a widely studied elementary tree operation. Combining concepts on rotation distance and data structures we give a basic algorithm that performs the transformation in Θ(n) time and Θ(1) space, making at most 2n...

We give linear-time algorithms for re-ordering and heightrestricting a binary search tree with only a small increase in cost, constructing a nearly optimal binary search tree given the rank by probability of each possible outcome, and height-restricting an optimal binary search tree when the increase in cost is restricted. Whereas most algorithms for constructing good binary search trees need t...