We propose a format of a binary phrase structure grammar with composite labels. The grammar adopts binary rules so that the dependency between two sub-trees can be represented in the label of the tree. The label of a tree is composed of two attributes, each of which is extracted from each sub-tree, so that it can represent the compositional information of the tree. The composite label is genera...

An amortized analysis of the insertion and deletion algorithms of k-dimensional balanced binary trees (kBB-trees) is performed. It is shown that the total rebalancing time for a mixed sequence of m insertions and deletions in a kBB-tree of size n is O(k(m+n)). Based on 2BB-trees, a self-organizing tree, called a self-organizing balanced binary tree, is defined. It is shown that the average acce...

Introduced a new binary search tree algorithm, cache-splay, that was the first to achieve the Unified Bound of Iacono since this problem was posed in 2001, and showed that the lower bound framework (see below) applied to a more general model of computation than binary search. Additionally, my thesis summarized my previous work on developing both lower bounds and upper bounds on the cost of sequ...

Trees are a common structure to represent the inter-task communication pattern of a parallel algorithm. In this paper, we consider the embedding a complete binary tree in a star graph with the objective of minimizing congestion and dilation. We develop two embeddings: i) a congestion-free, dilation-2, load-1 embedding of a level-p binary tree, and ii) a congestion-free, dilation-2, load-2 k emb...

In this paper we are concerned with the analysis of special recursive algorithms for traversing the nodes of a planted plane tree (ordered tree ; planar tree) . Some by now classical results in this area are due to (de Bruijn, Knuth, and Rice, 1972 ; Knuth, 1973 ; Flajolet, 1981 ; Flajolet and Odlyzko, 1982 ; Flajolet, Raoult, and Vuillemin, 1979 ; Kemp, 1979) and others and are summarized in t...

This paper proposes a new coding scheme and an algorithm to determine ancestordescendant relationship among nodes in a tree without tree traversal. Each node in a tree is assigned a unique binary code. The algorithm and the binary coding approach were tested with trees of different heights and widths. The algorithm is of O(1) complexity versus O(d) for tree traversal, where d is the depth of th...

This article is a continuation of an article on deening functions on trees (see 7]). In this article we develop terminology specialized for binary trees, rst deening binary trees and binary grammars. We recast the induction principle for the set of parse trees of binary grammars and the scheme of deening functions inductively with the set as domain. We conclude with deening the scheme of deenin...

The rank/activity restriction on binary resolution is introduced. It accepts only a single derivation tree from a large equivalence class of such trees. The equivalence classes capture all trees that are the same size and differ only by reordering the resolution steps. A proof procedure that combines this restriction with the authors’ minimal restriction of binary resolution computes each minim...

A 2-binary tree is a binary rooted tree whose root is colored black and the other vertices are either black or white. We present several bijections concerning different types of 2-binary trees as well as other combinatorial structures such as ternary trees, non-crossing trees, Schröder paths, Motzkin paths and Dyck paths. We also obtain a number of enumeration results with respect to certain st...

Fast multiplication can be constructed by combining the tree structure of multiplication's addition, i.e. Wallace tree, with the parallel on-they conversion to have a multiplication without using any carry propagation adder at the end. This parallel on-they conversion speeds up the conversion of redundant binary to conventional binary. With the delay of n 4 , we can have the conversion from red...