INTRODUCTION Graph drawing addresses the problem of constructing geometric representations of graphs, and has important applications to key computer technologies such as software engineering, database systems, visual interfaces, and computer-aided-design. Research on graph drawing has been conducted within several diverse areas, including discrete mathematics (topological graph theory, geometric graph theory, order theory), algorithmics (graph algorithms, data structures, computational geometry, vlsi), and human-computer interaction (visual languages, graphical user interfaces, software visualization). This chapter overviews aspects of graph drawing that are especially relevant to computational geometry. Basic definitions on drawings and their properties are given in Section 1.1. Bounds on geometric and topological properties of drawings (e.g., area and crossings) are presented in Section 1.2. Section 1.3 deals with the time complexity of fundamental graph drawin

In order to realise the potential benefits of three--dimensional (3D) display of relational information, there is a need for effective 3D human--computer interface designs. Algorithms for automatically creating 3D visual representations of relational information are a significant component of these interfaces. One productive strategy for developing such algorithms has been via the graph as an intermediate representation of the relational information: the information is first expressed as a graph and then a layout algorithm is used to create a visual representation of the graph. This thesis examines some technical issues which arise when several common layout algorithms, developed originally for 2D display of graphs, are extended specifically to 3D display. Typical computer graphics display systems can only provide a limited resolution and display area. This places a limit on the size of graph which can be displayed effectively. Simplification of the graph can permit the display of lar...

Online Graph Drawing deals with huge graphs which are partially unknown. At any time, a tiny part of the graph is displayed on the screen. Examples include WWW graphs and graphs of links in distributed file systems. This paper discusses issues arising in the presentation of such graphs. The paper describes a system for dealing with WWW graphs using Online Graph Drawing. Keywords: graph drawing, information visualization, computer graphics. 1 Introduction As graphics workstations have now become common tools for software and information engineers, visualization of relational information has become an essential element of current software systems. Examples include web browsers, file system visualizers, CASE tools, database design systems, network design systems, visual programming interfaces, and reverse engineering systems. The effectiveness of visualizing relational information is widely recognized. Most systems use graphs to model relational structures: the entities are nodes, and th...

Abstract. Graphs are widely used for information visualization purposes, since they provide a natural and intuitive representation of complex abstract structures. The automatic generation of drawings of graphs has applications a variety of fields such as software engineering, database systems, and graphical user interfaces. In this paper, we survey algorithmic techniques for graph drawing that support the expression and satisfaction of user-defined constraints. 1.

This paper and the accompanying demo describe a strategy and a software architecture for integrating several declarative approaches. This architecture allows for the interactive specification of local criteria for each vertex and edge. The Gold

We propose a new framework for the layout of graphs, which both unifies and generalizes many approaches known from the literature. Doing so, we briefly survey a number of models, particularly including force directed placement approaches. Our model is based on the stochastic concept of random fields, which have applications in various other areas such as physics, biology, economics, or medical imaging. By allowing, yet not enforcing, the decoupling of model and computation, it integrates algorithmic and declarative approaches to graph layout. 1 Introduction Graphs are an abstraction that is central to computer science and many other disciplines. To communicate and explore graphs visually, drawings that obey domain specific aspects of expressiveness and readability are sought. Graph drawing, even for graphs of moderate size, is a tedious task that calls for automatic help. The growing literature on graph drawing is surveyed in [DETT94]. Generally speaking, existing approaches are divid...

A set of fundamental types of high-level interaction with diagrams is proposed. VIM, a prototype KBS with a 3D cooperative diagram as its user interface illustrates different layers of cooperation reflecting this classification. Also a number of ways in which 3D aids such cooperation are identified.

VIM demonstrates a 3D interactive diagram serving as a radically co-operative user interface to an Underlying Knowledge Base System (UKBS). VIM comprises a Prolog client linked by the Internet to a diagram graphics server linked by X/Motif to conventional 2D display hardware. The diagram integrates three concurrent layers of mixed-initiative, direct-manipulation interaction: (i) User-UKBS dialogue controlling beliefs presented in the diagram; (ii) Shared user-UKBS `browsing', controlling selectively emphasised selective viewing of a potentially much larger belief structure; (iii) Novel co-operative force-directed management of diagram layout. VIM's 3D diagrams have a constraining 3D spatial arrangement scheme and a fixed principal view. Subjectively this arrangement aids expressiveness, comprehensibility and perceptual toleration of both link crossings and topological change in the 2D display, and inhibits browsing disorientation. We argue that this style of interface offers fundamental benefits to knowledge engineers and end users.

Introduction The research concerned the design and demonstration of Diagrammatic User Interfaces (DUIs) [28] for Knowledge Based Systems (KBSs) exhibiting: ffl Direct-manipulation consultation of the KBS; ffl Multi-focal browsing of its knowledge diagram; ffl Co-operative management of the diagram layout; ffl Applicability in KBS engineering and end-use; ffl Extensibility to handle large knowledge bases; ffl Accessibility on conventional Unix workstations; ffl The leverage of Logic Programming. As such the research has also addressed: ffl Understanding user's requirements and tasks; ffl User interaction designs (spatial organisation, metaphors, manipulations, dynamics); ffl User-interaction design methods (CHCID); ffl User interface architecture and implementation, geared to providing a Prolog KBS environment exploiting distr

: A general overview of the problem of automatically generating aesthetically pleasing drawings of graphs is presented. Requirements particular to diagrams in Rational Rose is discussed. The Sugiyama layout algorithm and the Spring Embedder algorithm together with a number of proposed modifications and improvements to these algorithms are discussed. Examples of drawings generated by these algorithms are presented. Automatic layout of diagrams through the use of genetic algorithms is also discussed. Supervisor: Gunnar Blomberg, Rational Software Scandinavia AB Examiner: Mats Nordstrm, Computing Science Dept., Uppsala University Passed: Contents 1 Introduction 1 1.1 Definition of Terms 2 1.2 Background 3 1.3 Problem Description 4 1.4 General Difficulties 6 2 Different Approaches 7 2.1 Algorithmic Approach 7 2.2 Declarative Approach 8 3 Examples of Algorithmic Approaches 9 3.1 Sugiyama Algorithm 9 3.1.1 Phase 1 Revisited -- Preprocessing 10 3.1.2 Phase 2 Revisited -- Edge Crossing Mini...