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Motion planning in the presence of obstacles deals with finding efficient paths from source to target which avoid hitting any of the obstacles. Applications include motion planning in robotics and designing efficient routing systems.Theoretical concepts from graph theory, topology, and computational geometry form the basis for some of the algorithms used in motion planning. The visibility graph is a standard model used in the study of motion planning.This thesis is a report of the research project undertaken to study visibility graphs and their applications to motion planning for certain geometric objects: polygons, line segments and points.The thesis consists of two parts.Theory: This part contains the details of topics from graph theory, topology, and computational geometry in motion planning. It also includes new algorithms which were developed as a part of this thesis.Implementation: This part describes a software system to implement the theory as an example of real applications. This software also includes many tools which help in studying visibility graphs. / Department of Computer Science

Integrity was invented to be a realistic measure of how difficult it is to break up a graph into small pieces by removing some of its elements. There are many different types of integrity, but in general it is defined as the minimum possible sum of two numbers: a number indicating the number of elements that are removed from the graph, and a number reflecting the size of the largest group of elements that remain connected despite this removal.This thesis consists of a study of the known results in three varieties of graph integrity (vertex integrity, edge integrity, and pure integrity), and an attempt to add to this knowledge. Many of these results have been integrated into a computer program.The computer program is designed to be useful as an aid in studying and teaching integrity. It allows the researcher to draw a graph and then select among a number of algorithms for computing or finding bounds for these varieties of integrity. / Department of Computer Science

Given a finite set S of n nonintersecting line segments with no three end points collinear, the segment end point visibility graph is defined as the graph whose vertices are the end points of the line segments in S and two vertices are adjacent if the straight line segment joining two end points does not intersect any element of S, or if they are end points of the same segment. Segment end point visibility graphs have a wide variety of applications in VLSI circuit design, study of art gallery problems, and other areas of computational geometry. This thesis contains a survey of the important results that are currently known regarding the characterization of these graphs. Also a weak visibility dual of a segment end point visibility graph is defined and some structural properties of such graphs are presented. Some open problems and questions related to the characterization of weak visibility graphs are also discussed. / Department of Mathematical Sciences

Segment endpoint visibility graph is a representation scheme for art gallery problems, guard problems, and other shortest path or shortest circuit problems. In the research of visibility graphs, drawing graphs is a time-consuming task. VGE (Visibility Graphs Editor) is developed for visibility graphs reseacheres to create and modify graphs interactively in X-window environment. Appropriate graphics user interface allows the researcher to edit a graph, save and open a file, and make a hard copy of a graph. VGE is developed in C under X-window environment and using EZD[3] graphics tool. The thesis also discusses the uses of EZD. Although it is still only a prototype, VGE is a successful tool for analyzing visibility graphs. / Department of Computer Science

Bibliography: leaves 150-161. / xvi, 161 leaves : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis addresses two areas in the field of conceptual structures. The first is the unification of conceptual graphs, and the consequent work in projection and in type hierarchies... The second area of investigation is the definition of constraints, especially real-value constraints on the concept referents, with particular attention to handling constraints during the unification of conceptual graphs. / Thesis (Ph.D.)--University of Adelaide, Dept. of Computer Science, 2001

Thesis (Ph. D.)--Illinois State University, 2007. / Title from title page screen, viewed on April 8, 2008. Dissertation Committee: Edward S. Mooney (chair), Cynthia W. Langrall, Sherry L. Meier, Norma C. Presmeg. Includes bibliographical references (leaves 112-121) and abstract. Also available in print.

Thesis (Ph.D.) -- University of Adelaide, Dept. of Computer Science, 2001. / Bibliography: leaves 150-161.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [91]-94).

Thesis (MS)--Montana State University--Bozeman, 2008. / Typescript. Chairperson, Graduate Committee: Rafal A. Angryk. Includes bibliographical references (leaves 59-65).