Time-Optimal Tree Computations on Sparse Meshes

The main goal of this work is to fathom the suitability of the mesh with multiple broadcasting architecture (MMB) for some tree-related computations. We view our contribution at two levels: on the one hand, we exhibit time lower bounds for a number of tree-related problems on the MMB. On the other hand, we show that these lower bounds are tight by exhibiting time-optimal tree algorithms on the MMB. Specifically, we show that the task of encoding and/or decoding n-node binary and ordered trees cannot be solved faster than Ω(log n) time even if the MMB has an infinite number of processors. We then go on to show that this lower bound is tight. We also show that the task of reconstructing n-node binary trees and ordered trees from their traversais can be performed in O(1) time on the same architecture. Our algorithms rely on novel time-optimal algorithms on sequences of parentheses that we also develop

Geometric modeling for computer aided design

The primary goal of this grant has been the design and implementation of software to be used in the conceptual design of aerospace vehicles particularly focused on the elements of geometric design, graphical user interfaces, and the interaction of the multitude of software typically used in this engineering environment. This has resulted in the development of several analysis packages and design studies. These include two major software systems currently used in the conceptual level design of aerospace vehicles. These tools are SMART, the Solid Modeling Aerospace Research Tool, and EASIE, the Environment for Software Integration and Execution. Additional software tools were designed and implemented to address the needs of the engineer working in the conceptual design environment. SMART provides conceptual designers with a rapid prototyping capability and several engineering analysis capabilities. In addition, SMART has a carefully engineered user interface that makes it easy to learn and use. Finally, a number of specialty characteristics have been built into SMART which allow it to be used efficiently as a front end geometry processor for other analysis packages. EASIE provides a set of interactive utilities that simplify the task of building and executing computer aided design systems consisting of diverse, stand-alone, analysis codes. Resulting in a streamlining of the exchange of data between programs reducing errors and improving the efficiency. EASIE provides both a methodology and a collection of software tools to ease the task of coordinating engineering design and analysis codes

Fast Parallel Algorithms for Basic Problems

Parallel processing is one of the most active research areas these days. We are interested in one aspect of parallel processing, i.e. the design and analysis of parallel algorithms. Here, we focus on non-numerical parallel algorithms for basic combinatorial problems, such as data structures, selection, searching, merging and sorting. The purposes of studying these types of problems are to obtain basic building blocks which will be useful in solving complex problems, and to develop fundamental algorithmic techniques. In this thesis, we study the following problems: priority queues, multiple search and multiple selection, and reconstruction of a binary tree from its traversals. The research on priority queue was motivated by its various applications. The purpose of studying multiple search and multiple selection is to explore the relationships between four of the most fundamental problems in algorithm design, that is, selection, searching, merging and sorting; while our parallel solutions can be used as subroutines in algorithms for other problems. The research on the last problem, reconstruction of a binary tree from its traversals, was stimulated by a challenge proposed in a recent paper by Berkman et al. ( Highly Parallelizable Problems, STOC 89) to design doubly logarithmic time optimal parallel algorithms because a remarkably small number of such parallel algorithms exist

Geometric modeling for computer aided design

Over the past several years, it has been the primary goal of this grant to design and implement software to be used in the conceptual design of aerospace vehicles. The work carried out under this grant was performed jointly with members of the Vehicle Analysis Branch (VAB) of NASA LaRC, Computer Sciences Corp., and Vigyan Corp. This has resulted in the development of several packages and design studies. Primary among these are the interactive geometric modeling tool, the Solid Modeling Aerospace Research Tool (smart), and the integration and execution tools provided by the Environment for Application Software Integration and Execution (EASIE). In addition, it is the purpose of the personnel of this grant to provide consultation in the areas of structural design, algorithm development, and software development and implementation, particularly in the areas of computer aided design, geometric surface representation, and parallel algorithms