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...

Most information retrieval systems are comprised of a focused set of domain-specific documents located within a single logical repository. A mechanism is developed by which user queries against such a system are used to generate a concept hierarchy pertinent to the domain. First, an algorithm is described which extracts terms from documents matching user queries, and then reduces this set of te...

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...

In this paper, we study data structures for N-body simulation. The basic data structure is a hierarchical partition of the input which is used for clustering particles in order to perform an eecient force computation. We are interested in Nearest Neighbor Trees which are formed by repeatedly combining mutually closest pairs of points to create a binary tree. This data structure is an alternativ...

Due to myriads of classes, designing accurate and efficient classifiers becomes very challenging for multi-class classification. Recent research has shown that class structure learning can greatly facilitate multi-class learning. In this paper, we propose a novel method to learn the class structure for multi-class classification problems. The class structure is assumed to be a binary hierarchic...

Decision trees are probably the most popular and commonly used classification model. They are recursively built following a top-down approach (from general concepts to particular examples) by repeated splits of the training dataset. When this dataset contains numerical attributes, binary splits are usually performed by choosing the threshold value which minimizes the impurity measure used as sp...

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...