Optimal binary trees with height restrictions on left and right branches

We begin with background definitions on binary trees. Then we review known algorithms for finding optimal binary search trees. Knuth\u27s famous algorithm, presented in the second chapter, is the cornerstone for our work. It depends on two important results: the Quadrangle Lemma and the Monoticity Theorem. These enabled Knuth to achieve a time complexity of O(n2), while previous algorithms had been O(n3) (n = size of input). We present the known generalization of Knuth\u27s algorithm to trees with a height restriction. Finally, we consider the previously unexamined case of trees with different restrictions on left and right heights. We prove the Quadrangle Lemma and the Monoticity Theorem in this case, and present an algorithm based on this

Efficient Data Structures and Algorithms for Scientific Computations.

Large-scale numerically intensive scientific applications can require tremendous amounts of computer time and space. Two general methods are presented for reducing the computer resources required in scientific computing. The first is a numerical database system which is built on a space and time optimal data structure called a weighted search tree and that allows for the storage and retrieval of valuable intermediate information so costly redundant calculations can be avoided. The second is a matrix algorithm based on a new space optimal representation of sparse matrices that for typical scientific applications can be expected to dramatically decrease the cost of multiplying sparse matrices. Codes and tests for each are given. Both methods can be implemented in a broad range of large-scale scientific applications

Efficient Linked List Ranking Algorithms and Parentheses Matching as a New Strategy for Parallel Algorithm Design

The goal of a parallel algorithm is to solve a single problem using multiple processors working together and to do so in an efficient manner. In this regard, there is a need to categorize strategies in order to solve broad classes of problems with similar structures and requirements. In this dissertation, two parallel algorithm design strategies are considered: linked list ranking and parentheses matching

Efficient Algorithms to Globally Balance a Binary Search Tree

A binary search tree can be globally balanced by readjustment of pointers or with a sorting process in O(n) time, n being the total number of nodes. This paper presents three global balancing algorithms, one of which uses folding with the other two adopting parallel procedures. These algorithms show improvement in time efficiency over some sequential algorithms when applied to large binary search trees. A comparison of various algorithms is presente