A methodology for 2D and 3D collision free path planning algorithm in a structured environment is presented. The isolated free convex areas are represented as a nodes in a graph, and a graph traversal strategy that dynamically allocates costs to graph path is used. Modification of the algorithm for small computational time and optimality is discussed. The 3D path planning is done in the three orthogonal two-dimensional projections of a 3D environment. Collision checking to increase the optimality for 3D paths is done in each of the three orthogonal two-dimensional subspaces.

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The GLuskap system for interactive three-dimensional graph drawing applies techniques of scientific visualization and interactive systems to the construction, display, and analysis of graph drawings. Important features of the system include support for large-screen stereographic 3D display with immersive head-tracking and motion-tracked interactive 3D wand control. A distributed rendering architecture contributes to the portability of the system, with user control performed on a laptop computer without specialized graphics hardware. An interface for implementing graph drawing layout and analysis algorithms in the Python programming language is also provided. This thesis describes comprehensively the work on the system by the author—this work includes the design and implementation of the major features described above. Further directions for continued development and research in cognitive tools for graph drawing research are also suggested. / viii, 110 leaves : ill. (some col.) ; 29 cm.

Thesis (Ph.D.)--Computing, Georgia Institute of Technology, 2009. / Committee Chair: Bader, David; Committee Member: Berry, Jonathan; Committee Member: Fujimoto, Richard; Committee Member: Saini, Subhash; Committee Member: Vuduc, Richard

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This thesis describes the development of the SmartGraph, an AI enabled graph database. The need for such a system has been independently recognized in the isolated fields of graph databases, graph computing, and computational graph deep learning systems, such as TensorFlow. Though prior works have investigated some relationships between these fields, we believe that the SmartGraph is the first system designed from conception to incorporate the most significant and useful characteristics of each. Examples include the ability to store graph structured data, run analytics natively on this data, and run gradient descent algorithms. It is the synergistic aspects of combining these fields that provide the most novel results presented in this dissertation. Key among them is how the notion of “graph querying” as used in graph databases can be used to solve a problem that has plagued deep learning systems since their inception; rather than attempting to embed graph structured datasets into restrictive vector spaces, we instead allow the deep learning functionality of the system to natively perform graph querying in memory during optimization as a way of interpreting (and learning) the graph. This results in a concept of natural and interpretable processing of graph structured data. Graph computing systems have traditionally used distributed computing across multiple compute nodes (e.g. separate machines connected via Ethernet or internet) to deal with large-scale datasets whilst working sequentially on problems over entire datasets. In this dissertation, we outline a distributed graph computing methodology that facilitates all the above capabilities (even in an environment consisting of a single physical machine) while allowing for a workflow more typical of a graph database than a graph computing system; massive concurrent access allowing for arbitrarily asynchronous execution of queries and analytics across the entire system. Further, we demonstrate how this methodology is key to the artificial intelligence capabilities of the system.

Image representation plays an important role in image processing applications, which usually. contain a huge amount of data. An image is a two-dimensional array of points, and each point contains information (eg: color). A 1024 by 1024 pixel image occupies 1 mega byte of space in the main memory. In actual circumstances 2 to 3 mega bytes of space are needed to facilitate the various image processing tasks. Large amounts of secondary memory are also required to hold various data sets. In this thesis, two different operations on the quadtree are presented. There are, in general, two types of data compression techniques in image processing. One approach is based on elimination of redundant data from the original picture. Other techniques rely on higher levels of processing such as interpretations, generations, inductions and deduction procedures (1, 2). One of the popular techniques of data representation that has received a considerable amount of attention in recent years is the quadtree data structure. This has led to the development of various techniques for performing conversions and operations on the quadtree. Klinger and Dyer (3) provide a good bibliography of the history of quadtrees. Their paper reports experiments on the degree of compaction of picture representation which may be achieved with tree encoding. Their experiments show that tree encoding can produce memory savings. Pavlidis [15] reports on the approximation of pictures by quadtrees. Horowitz and Pavidis [16] show how to segment a picture using traversal of a quadtree. They segment the picture by polygonal boundaries. Tanimoto [17] discusses distortions which may occur in quadtrees for pictures. Tanimoto [18, p. 27] observes that quadtree representation is particularly convenient for scaling a picture by powers of two. Quadtrees are also useful in graphics and animation applications [19, 20] which are oriented toward construction of images from polygons and superpositiofis of images. Encoded pictures are useful for display, especially if encoding lends itself to processing.

G-Net system is being developed by the members of the G-Net research group under the supervision of Dr. K. Jay Bagga. The principle objective of the G-Net system is to provide an integrated tool for dealing with various aspects of graph theory. G-Net system is divided into two parts. GETS (Graph theory Experiments Tool Set) will provide a set of tools to experiment with graph theory, and HYGRES (HYpertext Graph theory Reference Service), the second subcomponent of the G-Net system to aid graph theory study and research. In this research a hypertext application is built to present the graph theory concepts, graph models and the algorithms. In other words, HYGRES (Guide Version) provides the hypertext facilities for organizing a graph theory database in a very natural and interactive way. An hypertext application development tool, called Guide, is used to implement this version of HYGRES. This project integrates the existing version of GETS so that it can also provide important services to HYGRES. The motivation behind this project is to study the initial criterion for developing a hypertext system, which can be used for future development of a stand alone version of the G-Net system. / Department of Computer Science

Many areas of computer science use graph theory and thus benefit from research in graph theory. Some of the important activities involved in graph theory work are the study of concepts, algorithm development, and theorem proving. These can be facilitated by providing computerized tools for graph drawing, algorithm animation and accessing graph theory information bases. Project G-Net is aimed at developing a set of such tools.Project G-Net has chosen to provide the tools in hypertext form based on the analysis of users' requirements. The project is presently developing a hypertext application and a hypertext system for providing the above set of tools. In the process of this development various issues pertaining to hypertext authoring, hypertext usability and application of graph theory to hypertext are being explored.The focus of this thesis is in proving that hypertext approach is most appropriate for realizing the goals of the G-Net project. The author was involved in the research that went into analysis of requirements, design of hypertext application and system, and the investigation of the complementary relationship between graph theory and hypertext. / Department of Computer Science

M.Sc. (Computer Science) / Please refer to full text to view abstract