Tesi sul tema "Graphic methods"

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.<br>Department of Computer Science

ENGLISH ABSTRACT: Determining the (classical) chromatic number of a graph (i.e. finding the smallest number of colours with which the vertices of a graph may be coloured so that no two adjacent vertices receive the same colour) is a well known combinatorial optimization problem and is widely encountered in scheduling problems. Since the late 1960s the notion of the chromatic number has been generalized in several ways by relaxing the restriction of independence of the colour classes.<br>AFRIKAANSE OPSOMMING: Die bepaling van die (klassieke) chromatiese getal van ’n grafiek (naamlik die kleinste aantal kleure waarmee die punte van ’n grafiek gekleur kan word sodat geen twee naasliggende punte dieselfde kleur ontvang nie) is ’n bekende kombinatoriese optimeringsprobleem wat wyd in skeduleringstoepassings te¨egekom word. Sedert die laat 1960s is die definisie van die chromatiese getal op verskeie maniere veralgemeen deur die vereiste van onafhanklikheid van die kleurklasse te verslap.<br>Thesis (DPhil)--Stellenbosch University, 2007.

Ordinary graphs are directed graphs that can be viewed as generalizations of symmetric block designs. They were introduced by Fossorier, Jezek, Nation and Pogel in [2] in an attempt to construct new finite projective planes. In this thesis we investigate some special cases of ordinary graphs, most prominently the case where nonadjacent vertices have no common neighbors. We determine all connected graphs of this type that exist.<br>vii, 65 leaves, bound ; 29 cm.<br>Thesis (Ph. D.)--University of Hawaii at Manoa, 2005.

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.<br>Department of Mathematical Sciences

Graph visualization plays an increasingly important role in software engineering and information systems. Examples include UML, E-R diagrams, database structures, visual programming, web visualization, network protocols, molecular structures, genome diagrams, and social structures. Many classical algorithms for graph visualization have already been developed over the past decades. However, these algorithms face difficulties in practice, such as the overlapping nodes, large graph layout, and dynamic graph layout. In order to solve these problems, this research aims to systematically address both algorithmic and approach issues related to a novel framework that describes the process of graph visualization applications. At the same time, all the proposed algorithms and approaches can be applied to other situations as well. First of all, a framework for graph visualization is described, along with a generic approach to the graphical representation of a relational information source. As the important parts of this framework, two main approaches, Filtering and Clustering, are then particularly investigated to deal with large graph layouts effectively. In order to filter 'noise' or less important nodes in a given graph, two new methods are proposed to compute importance scores of nodes called NodeRank, and then to control the appearances of nodes in a layout by ranking them. Two novel algorithms for clustering graphs, KNN and SKM, are developed to reduce visual complexity. Identifying seed nodes as initial members of clusters, both algorithms make use of either the k-nearest neighbour search or a novel node similarity matrix to seek groups of nodes with most affinities or similarities among them. Such groups of relatively highly connected nodes are then replaced with abstract nodes to form a coarse graph with reduced dimensions. An approach called MMD to the layout of clustered graphs is provided using a multiple-window�multiple-level display. As for the dynamic graph layout, a new approach to removing overlapping nodes called Force-Transfer algorithm is developed to greatly improve the classical Force- Scan algorithm. Demonstrating the performance of the proposed algorithms and approaches, the framework has been implemented in a prototype called PGD. A number of experiments as well as a case study have been carried out.

This practice-led research is the result of an interest in graphic design as a specific critical activity. Existing in the context of the 2008 financial and subsequent political crisis, both this thesis and my work are situated in an expaded field of graphic design. This research examines the emergence of the terms critical design and critical practice,and aims to develop methods that use criticism during the design process from a practitioner’s perspective. Central aims of this research are to address a gap in design discourse in relation to this terminology and impact designers operating under the banner of such terms, as well as challenging practitioners to develop a more critical design practice. The central argument of this thesis is that in order to develop a critical practice, a designer must approach design as criticism. Adopting a mixed methods approach to research, this thesis draws on 'action research'(Schön, 1983) and is aligned with the proposition of ‘problem setting’ instead of the established ‘problem solving’ approach to design, using the following methods: 1)workshops at the Royal College of Art, Sandberg Institute, University of Westminster and London College of Communication; 2) selection of projects from professional practice; 3) self-initiated research projects; 4) critical writing, including essays, reviews,interviews and in particular the publication 'Modes of Criticism'. Following the theorisation of the terms critical design and critical practice, historical survey of criticism, politics and ideology in relation to graphic design, and reflection on the workshops and methods detailed above, this thesis proposes a critical method consisting of three dimensions: visual criticality, critical reflexivity and design fiction. It argues that criticism as design method offers a fundamental opportunity to develop a reflected and critical approach to design, and more importantly, society. This method creates opportunities to develop a critical practice; one that shapes a continuous agency and interest in wicked, systemic and infrastructural problems with a constant ability to critically adapt and research their multi-layered nature. That will on the one hand help the designer to become a substantial agent of change and on the other, in particularly difficult circumstances of conflicted personal, private, disciplinary and public interest such as commercial practice, to find opportunities for criticality.

Graphs, as mathematical objects, play a dominant role in the study of network modeling, VLSI design, data structures, parallel computation, process scheduling and in a variety of other areas of computer science. Hypercubes are one of the preferred architectures for parallel computation, and a study of some properties of the hypercubes motivated this thesis.The concept of super line graphs, introduced by Bagga at el, generalizes the notion of line graphs. In this thesis several graph theoretic properties of super line graphs of hypercubes are studied. In particular the super line graphs of index two of hypercubes are investigated and some exact results and precise characterizations are found.<br>Department of Computer Science

This research aims to apply procedural techniques, similar to those employed in node-based modeling or compositing software packages, to the motion design workflow in Adobe After Effects. The purpose is to increase efficiency in the motion design process between pre-production and production stages. Systems Theory is referenced as a basis for breaking down problems in terms of inputs and outputs. All of this takes place within the context of a larger motion design project.

Thesis (M.S.)--West Virginia University, 2002.<br>Title from document title page. Document formatted into pages; contains vi, 96 p. : ill. Includes abstract. Includes bibliographical references (p. 91-96).

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.<br>viii, 110 leaves : ill. (some col.) ; 29 cm.

A 3D arrangement graph G is the abstract graph induced by an arrangement of planes in general position where the intersection of any two planes forms a line of intersection and an intersection of three planes creates a point. The properties of three classes of arrangement graphs — four, five and six planes — are investigated. For graphs induced from six planes, specialized methods were developed to ensure all possible graphs were discovered. The main results are: the number of 3D arrangement graphs induced by four, five and six planes are one, one and 43 respectively; the three classes are Hamiltonian; and the 3D arrangement graphs created from four and five planes are planar but none of the graphs created from six planes are planar.<br>x, 89 leaves : ill. (some col.) ; 29 cm

This thesis report introduces a new technique of document clustering based on frequent senses. The developed system, named GDClust (Graph-Based Document Clustering) [1], works with frequent senses rather than dealing with frequent keywords used in traditional text mining techniques. GDClust presents text documents as hierarchical document-graphs and uses an Apriori paradigm to find the frequent subgraphs, which reflect frequent senses. Discovered frequent subgraphs are then utilized to generate accurate sense-based document clusters. We propose a novel multilevel Gaussian minimum support strategy for candidate subgraph generation. Additionally, we introduce another novel mechanism called Subgraph-Extension mining that reduces the number of candidates and overhead imposed by the traditional Apriori-based candidate generation mechanism. GDClust utilizes an English language thesaurus (WordNet [2]) to construct document-graphs and exploits graph-based data mining techniques for sense discovery and clustering. It is an automated system and requires minimal human interaction for the clustering purpose.

Bibliography: leaves 150-161. 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.

The purpose of this study was to investigate the effectiveness of the graphing calculator on the achievement, attitude toward mathematics, and confidence in learning mathematics of Algebra II students.

The effectiveness of selected computer-generated graphics display variables was examined in a mixed-factors factorial experiment using thirty-two subjects. All subjects performed four different graph reading tasks consisting of point-reading, point-comparison, trendreading, and trend-comparison. In each task, line, point, bar, and three-dimensional bar graphs were investigated under two levels of task complexity, and two levels of coding (color and black-and-white). The effects of these independent variables on measures of task performance errors, time to complete the task, subjective mental workload, and preference ratings were obtained in real-time by a microcomputer control program. Separate MANOVA analyses of these measures for each task indicated significant effects of graph-type for the point—reading task, main effects of complexity and coding for all tasks, and a graph-by—coding interaction for the point-reading, point-comparison, and trend-reading tasks. Subsequent ANOVA analyses showed significance for these effects across several of the dependent measures which are specified in the thesis. Recommendations are made for selecting the most effective graph and coding combinations for the particular types of graph-interpretation tasks and complexity levels encountered.<br>Master of Science

Thesis (M.S. in Operations Research)--Naval Postgraduate School, September 1990.<br>Thesis Advisor(s): Read, Robert R. ; Dryer, David A. Second Reader: Whitaker, Lyn R. "September 1990." DTIC Descriptor(s): Army Training, Combat Information Centers, Organizations, Training, Battalion Level Organizations, Battlefields, Task Forces, Attack, Missions, Standards, Graphics, Military Training, Archives, Combat Forces, Discriminate Analysis, Doctrine, Frequency, Data Processing. DTIC Identifier(s): National Training Center, Army Operation. Author(s) subject terms: National Training Center, Deliberate Attack, Operational. Description based on title screen as viewed on Dec. 22, 2009. Includes bibliographical references (p. 82). Also available in print.

In this project, an enhanced version of Jedit is presented. Jedit is a Graph Editor developed at Ball State University by a group of students under the direction of Dr. Jay Bagga. The following paper describes the new version, named Jedit 4.0.In this version two new algorithms are implemented. These are: Planarity Testing and Planarity Drawing. The first algorithm tests a graph for planarity and the second one makes a planar embedding of the graph in a grid of size (n-2) x (n-2), where n is the order of the graph. Planar graphs have important applications in the fields of computer engineering, architecture, and many others.Jedit 4.0 also includes new features that were not available in earlier versions. The new features include: graph rotation operation, graph complement, drawing of well-known graphs, and credits window. Several modifications and additions to existing features and algorithms have also been carried out.Jedit 4.0 uses swing java technology what provides a more elegant look. Drop down menus have also been added to provide the user an easier way to use Jedit.<br>Department of Computer Science

Dissertation (PhD)--Stellenbosch University, 2001.<br>ENGLISH ABSTRACT: Gower and Hand offer a new perspective on the traditional biplot. This perspective provides a unified approach to principal component analysis (PCA) biplots based on Pythagorean distance; canonical variate analysis (CVA) biplots based on Mahalanobis distance; non-linear biplots based on Euclidean embeddable distances as well as generalised biplots for use with both continuous and categorical variables. The biplot methodology of Gower and Hand is extended and applied in statistical discrimination and classification. This leads to discriminant analysis by means of PCA biplots, CVA biplots, non-linear biplots as well as generalised biplots. Properties of these techniques are derived in detail. Classification regions defined for linear discriminant analysis (LDA) are applied in the CVA biplot leading to discriminant analysis using biplot methodology. Situations where the assumptions of LDA are not met are considered and various existing alternative discriminant analysis procedures are formulated in terms of biplots and apart from PCA biplots, QDA, FDA and DSM biplots are defined, constructed and their usage illustrated. It is demonstrated that biplot methodology naturally provides for managing categorical and continuous variables simultaneously. It is shown through a simulation study that the techniques based on biplot methodology can be applied successfully to the reversal problem with categorical variables in discriminant analysis. Situations occurring in practice where existing discriminant analysis procedures based on distances from means fail are considered. After discussing self-consistency and principal curves (a form of non-parametric principal components), discriminant analysis based on distances from principal curves (a form of a conditional mean) are proposed. This biplot classification procedure based upon principal curves, yields much better results. Bootstrapping is considered as a means of describing variability in biplots. Variability in samples as well as of axes in biplot displays receives attention. Bootstrap a-regions are defined and the ability of these regions to describe biplot variability and to detect outliers is demonstrated. Robust PCA and CVA biplots restricting the role of influential observations on biplot displays are also considered. An extensive library of S-PLUS computer programmes is provided for implementing the various discriminant analysis techniques that were developed using biplot methodology. The application of the above theoretical developments and computer software is illustrated by analysing real-life data sets. Biplots are used to investigate the degree of capital intensity of companies and to serve as an aid in risk management of a financial institution. A particular application of the PCA biplot is the TQI biplot used in industry to determine the degree to which manufactured items comply with multidimensional specifications. A further interesting application is to determine whether an Old-Cape furniture item is manufactured of stinkwood or embuia. A data set provided by the Western Cape Nature Conservation Board consisting of measurements of tortoises from the species Homopus areolatus is analysed by means of biplot methodology to determine if morphological differences exist among tortoises from different geographical regions. Allometric considerations need to be taken into account and the resulting small sample sizes in some subgroups severely limit the use of conventional statistical procedures. Biplot methodology is also applied to classification in a diabetes data set illustrating the combined advantage of using classification with principal curves in a robust biplot or biplot classification where covariance matrices are unequal. A discriminant analysis problem where foraging behaviour of deer might eventually result in a change in the dominant plant species is used to illustrate biplot classification of data sets containing both continuous and categorical variables. As an example of the use of biplots with large data sets a data set consisting of 16828 lemons is analysed using biplot methodology to investigate differences in fruit from various areas of production, cultivars and rootstocks. The proposed a-bags also provide a measure of quantifying the graphical overlap among classes. This method is successfully applied in a multidimensional socio-economical data set to quantify the degree of overlap among different race groups. The application of the proposed biplot methodology in practice has an important byproduct: It provides the impetus for many a new idea, e.g. applying a peA biplot in industry led to the development of quality regions; a-bags were constructed to represent thousands of observations in the lemons data set, in tum leading to means for quantifying the degree of overlap. This illustrates the enormous flexibility of biplots - biplot methodology provides an infrastructure for many novelties when applied in practice.<br>AFRIKAANSE OPSOMMING: Gower en Hand bied 'n nuwe perspektief op die tradisionele bistipping. Hierdie perspektief verskaf 'n uniforme benadering tot hoofkomponent analise (HKA) bistippings gebaseer op Pythagoras-afstand; kanoniese veranderlike analise (KVA) bistippings gebaseer op Mahalanobis-afstand; nie-lineere bistippings gebaseer op Euclidies inbedbare afstande sowel as veralgemeende bistippings vir gebruik wanneer beide kontinue en kategoriese veranderlikes voorkom. Die bistippingsmetodologie van Gower en Hand word uitgebrei en toegepas in statistiese diskriminasie en klassifikasie. Dit lei tot diskriminantanalise met behulp van HKA bistippings, KVA bistippings, nie-lineere bistippings sowel as veralgemeende bistippings. Die eienskappe van hierdie tegnieke word in besonderhede afgelei. Die toepassing van die konsep van 'n klassifikasiegebied in die KVA bistipping baan die weg vir lineere diskriminantanalise (LDA) met behulp van bistippingsmetodologie. Situasies waar daar nie aan die aannames van LDA voldoen word nie kry aandag en verskeie bestaande altematiewe diskriminantanalise prosedures word in terme van bistippings geformuleer en naas HKA bistippings, word QDA, FDA en DSM bistippings gedefinieer, gekonstrueer en hul gebruike gedemonstreer. Dit word aangetoon dat bistippingsmetodologie op 'n natuurlik wyse voorsiening maak om kategoriese veranderlikes en kontinue veranderlikes gelyktydig te hanteer. Daar word met behulp van 'n simulasie-studie aangetoon dat tegnieke gebaseer op die bistippingsmetodologie wat ontwikkel IS, suksesvol by die sogenaamde ornkeringsprobleem by diskriminantanalise met kategoriese veranderlikes gebruik kan word. Verder word aangevoer dat daar baie praktiese situasies voorkom waar bestaande prosedures van diskriminantanalise faal omdat dit op afstande vanaf gemiddeldes gebaseer IS. Na 'n bespreking van self-konsekwentheid en hoofkrommes ('n vorm van nieparametriese hoofkomponente) word voorgestel om diskriminantanalise op afstand vanaf hoofkrommes ('n vonn van 'n voorwaardelike gemiddelde) te baseer. Sodoende is 'n bistippingklassifikasie prosedure wat op afstand vanaf hoofkrommes gebaseer is en wat baie beter resultate lewer, ontwikkel. Die variasie in die posisies van datapunte in die bistipping sowel as van die bistippingsasse word bestudeer met behulp van skoenlusmetodes. 'n Skoenlus a-gebied word gedefinieer en dit word gedemonstreer hoe so 'n a-gebied aangewend kan word om variasie in bistippings te beskryf en wegleers te identifiseer. Robuuste HKA en KV A bistippings wat die rol van invloedryke waamemings op die bistipping beperk, word bespreek. 'n Omvangryke biblioteek van S-PLUS rekenaarprogramme is geskryf VIr die implementering van die verskillende diskriminantanalise tegnieke wat met behulp van bistippingsmetodologie ontwikkel is. Die toepassing van die voorafgaande teoretiese ontwikkelinge en rekenaarprogramme word geillustreer aan die hand van werklike datastelle vanuit die praktyk. So word bistippings gebruik om die mate van kapitaalintensiteit van ondememings te ondersoek en om as hulpmiddel by risikobestuur van 'n finansiele instelling te dien. 'n Besondere toepassing van die HKA bistipping is die TQI bistipping wat in die industriele omgewing gebruik word ten einde te bepaal tot watter mate vervaardigde artikels aan neergelegde meerdimensionele spesifikasies voldoen. 'n Verdere interessante toepassing is om te bepaal of 'n Ou-Kaapse meubelstuk van stinkhout of embuia gemaak is. 'n Datastel verskaf deur Wes-Kaap Natuurbewaring in verband met die bekende padloper skilpad, Homopus areolatus, is met behulp van bistippings geanaliseer om te bepaal of daar morfometriese verskille tussen die padlopers afkomstig van bepaalde geografiese gebiede is. Allometriese beginsels moes ook in ag gene em word en die min waamemings in sommige van die subgroepe het tot gevolg dat konvensionele statistiese tegnieke nie sonder meer gebruik kan word nie. Die bistippingsmetodologie is ook toegepas op klassifikasie by 'n diabetes datastel om die gekombineerde gebruik van. hoofkrommes in 'n robuuste bistipping te illustreer en bistippingklassifikasie waar daar sprake van ongelyke kovariansiematrikse is. 'n Diskriminantanalise probleem waar die weidingsvoorkeure van wildsbokke 'n verandering in die dominante plantegroei tot gevolg kan he, word gebruik om bistippingklassifikasie met data waar kontinue sowel as kategoriese veranderlikes verskaf word, te illustreer. As voorbeeld van die gebruik van bistippings by 'n groot datastel is 'n datastel bestaande uit waamemings van 16828 suurlemoene met behulp van bistippingsmetodologie geanaliseer ten einde verskille in vrugte afkomstig van verskillende produsente-streke, kultivars en onderstamme te ondersoek. Die a-sakkies wat hier ontwikkel is, lei tot kwantifisering van die grafiese oorvleueling van groepe. Hierdie beginsel word suksesvol toegepas in 'n meerdimensionele sosio-ekonomiese datastel om die mate van oorvleueling van verskillende bevolkingsgroepe te kwantifiseer. Die toepassing van die voorgestelde bistippingsmetodologie in die praktyk lei tot 'n belangrike newe-produk: Dit verskaf die stimulus tot die ontstaan van nuwe idees, byvoorbeeld, die toepassing van 'n HKA bistipping in 'n industriele omgewing het tot die ontwikkeling van die konsep van 'n kwaliteitsgebied aanleiding gegee; a-sakkies is gekonstrueer om duisende waamemings in die suurlemoendatastel te verteenwoordig wat weer gelei het tot 'n metode om die graad van oorvleueling te kwantifiseer. Hierdeur is die geweldige veelsydigheid van bistippings geillustreer - bistippingsmetodologie verskaf die infrastruktuur vir baie vindingryke toepassings in die praktyk.

The purpose of this study was to investigate the effectiveness of carefully designed teacher training in the use of the computer to teach graphing skills associated with Algebra II conic sections. Three areas were studied: the teachers' attitude toward mathematics, and the effect on students' achievement in the area of graphing skills.

The strategy and change management fields have developed new perspectives in recent years. Studies show that a high percentage of strategic change efforts fail and it was argued that one problem was the unsuccessful communication of the vision and strategy to employees. This exploratory research studied the use of graphic facilitative methods within the context of an organisation's strategic change process. Phase one of the explorative study was carried out using the combination of interview data, workshops and literature to identify emerging themes and to develop a conceptual model. Phase two of the study was again exploratory but more focused on the themes that had emerged from the preliminary study. Data was collected through interviews, observational methods, survey and a more focused literature review. Through the combined findings of the preliminary and focused study and from the literature, the author established an understanding and theory of how the methods contribute to improved strategy communication. The research has re-enforced the view in literature that the strategy communication process will be more successful by ensuring the strategy is driven by the right people and the strategy development is realistic. The use of graphics, metaphors, stories and dialogue, in combination, can help to improve the strategy communication process by conveying a clear strategic message, by facilitating an interactive strategy communication process, by encouraging communication in an open and safe environment, and because they are new, innovative and different.

The hypercube is one of the most versatile and efficient networks yet discovered for parallel computation. It is well suited for both special-purpose and general-purpose tasks, and it can efficiently simulate many other networks of the same size. The size of subgraphs can be used to estimate the efficient communications of hypercube computer systems.The thesis investigates induced subgraphs of a hypercube, discusses sizes of subgraphs, and provides a formula to give bounds on the size of any subgraph of the hypercube.The concept of spanning graphs and line graphs is useful for studying properties of graphs. An MS WINDOWS based graphical system is developed which allows the creation and display of graphs and their spanning graphs, line graphs and super line graphs.<br>Department of Computer Science

This thesis explains to statisticians what graphical models are and how to use them for statistical inference; in particular, how to use decomposable graphical models for efficient inference in covariance selection and multivariate regression problems. The first aim of the thesis is to show that decomposable graphical models are worth using within a Bayesian framework. The second aim is to make the techniques of graphical models fully accessible to statisticians. To achieve these aims the thesis makes a number of statistical contributions. First, it proposes a new prior for decomposable graphs and a simulation methodology for estimating this prior. Second, it proposes a number of Markov chain Monte Carlo sampling schemes based on graphical techniques. The thesis also presents some new graphical results, and some existing results are reproved to make them more readily understood. Appendix 8.1 contains all the programs written to carry out the inference discussed in the thesis, together with both a summary of the theory on which they are based and a line by line description of how each routine works.

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.<br>Department of Computer Science

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.<br>Department of Computer Science

Thesis (PhD (Education))--University of Stellenbosch, 1998.<br>This dissertation deals with typical, widespread student errors with respect to kinematic graphs as revealed by a literature survey, as well as an own empirical investigation into the nature and extent of these misconceptions. The fact that certain misconceptions turned out to be more widespread than initially believed, has serious consequences for educators' assumptions about students' understanding of graphs in general, as well as their ideas on how to minimise some generally occurring "alternative views on graphs". Students' graphing skills are analysed and described in terms of a number of translations between various representations of physical events involving motion. A special focus is placed on graph transformations, which are translations from one graphical representation to another. It turned out that this provides valuable information about a learner's graphing skills, as well as his understanding of the relevant kinematic quantities and conventions required to make successful transformations.

Thesis (Ph. D.)--Washington State University, May 2009.<br>Title from PDF title page (viewed on June 3, 2009). "School of Electrical Engineering and Computer Science." Includes bibliographical references (p. 101-108).