A graph rewriting programming language for graph drawing

This paper describes Grrr, a prototype visual graph drawing tool. Previously there were no visual languages for programming graph drawing algorithms despite the inherently visual nature of the process. The languages which gave a diagrammatic view of graphs were not computationally complete and so could not be used to implement complex graph drawing algorithms. Hence current graph drawing tools are all text based. Recent developments in graph rewriting systems have produced computationally complete languages which give a visual view of graphs both whilst programming and during execution. Grrr, based on the Spider system, is a general purpose graph rewriting programming language which has now been extended in order to demonstrate the feasibility of visual graph drawing

Computing the Region Areas of Euler Diagrams Drawn with Three Ellipses

Ellipses generate accurate area-proportional Euler diagrams for more data than is possible with circles. However, computing the region areas is difficult as ellipses have various degrees of freedom. Numerical methods could be used, but approximation errors are introduced. Current analytic methods are limited to computing the area of only two overlapping ellipses, but area-proportional Euler diagrams in diverse application areas often have three curves. This paper provides an overview of different methods that could be used to compute the region areas of Euler diagrams drawn with ellipses. We also detail two novel analytic algorithms to instantaneously compute the exact region areas of three general overlapping ellipses. One of the algorithms decomposes the region of interest into ellipse segments, while the other uses integral calculus. Both methods perform equally well with respect to accuracy and time

A Graph Rewriting Visual Language for Database Programming

Textual database programming languages are computationally complete, but have the disadvantage of giving the user a non-intuitive view of the database information that is being manipulated. Visual languages developed in recent years have allowed naive users access to a direct representation of data, often in a graph form, but have concentrated on user interface rather than complex programming tasks. There is a need for a system which combines the advantages of both these programming methods. We describe an implementation of Spider, an experimental visual database programming language aimed at programmers. It uses a graph rewriting paradigm as a basis for a fully visual, computationally complete language. The graphs it rewrites represent the schema and instances of a database. The unique graph rewriting method used by Spider has syntactic and semantic simplicity. Its form of algorithmic expression allows complex computation to be easily represented in short programs. Furthermore, Spider has greater power than normally provided in textual systems, and we show that queries on the schema and associative queries can be performed easily and without requiring any additions to the language

Exploring Local Optima in Schematic Layout

In search-based graph drawing methods there are typically a number of parameters that control the search algorithm. These parameters do not affect the ?tness function, but nevertheless have an impact on the ?nal layout. One such search method is hill climbing, and, in the context of schematic layout, we explore how varying three parameters (grid spacing, the starting distance of allowed node movement and the number of iterations) affects the resultant diagram. Although we cannot characterize schematics completely and so cannot yet automatically assign parameters for diagrams, we observe that when parameters are set to values that increase the search space, they also tend to improve the ?nal layout. We come to the conclusion that hillclimbing methods for schematic layout are more prone to reaching local optima than had previously been expected and that a wider search, as described in this paper, can mitigate this, so resulting in a better layout

Gesture-Based Input for Drawing Schematics on a Mobile Device

We present a system for drawing metro map style schematics using a gesture-based interface. This work brings together techniques in gesture recognition on touch-sensitive devices with research in schematic layout of networks. The software allows users to create and edit schematic networks, and provides an automated layout method for improving the appearance of the schematic. A case study using the metro map metaphor to visualize social networks and web site structure is described

Improving Search-Based Schematic Layout by Parameter Manipulation

This paper reports on a method to improve the automated layout of schematic diagrams by widening the search space examined by the system. In search-based layout methods there are typically a number of parameters that control the search algorithm which do not affect the fitness function, but nevertheless have an impact on the final layout. We explore how varying three parameters (grid spacing, the starting distance of allowed node movement and the number of iterations) affects the resultant diagram in a hill- climbing layout system. Using an iterative process, we produce diagram layouts that are significantly better than those produced by ad-hoc parameter settings

Graph Algorithm Animation with Grrr

We discuss geometric positioning, highlighting of visited nodes and user defined highlighting that form the algorithm animation facilities in the Grrr graph rewriting programming language. The main purpose of animation was initially for the debugging and profiling of Grrr code, but recently it has been extended for the purpose of teaching algorithms to undergraduate students. The animation is restricted to graph based algorithms such as graph drawing, list manipulation or more traditional graph theory. The visual nature of the Grrr system allows much animation to be gained for free, with no extra user effort beyond the coding of the algorithm, but we also discuss user defined animations, where custom algorithm visualisations can be explicitly defined for teaching and demonstration purposes

Evaluating the Comprehension of Euler Diagrams

We describe an empirical investigation into layout criteria that can help with the comprehension of Euler diagrams. Euler diagrams are used to represent set inclusion in applications such as teaching set theory, database querying, software engineering, filing system organisation and bio-informatics. Research in automatically laying out Euler diagrams for use with these applications is at an early stage, and our work attempts to aid this research by informing layout designers about the importance of various Euler diagram aesthetic criteria. The three criteria under investigation were: contour jaggedness, zone area inequality and edge closeness. Subjects were asked to interpret diagrams with different combinations of levels for each of the criteria. Results for this investigation indicate that, within the parameters of the study, all three criteria are important for understanding Euler diagrams and we have a preliminary indication of the ordering of their importance

Representing Space: A Hybrid Genetic Algorithm for Aesthetic Graph Layout

This paper describes a hybrid Genetic Algorithm (GA) that is used to improve the layout of a graph according to a number of aesthetic criteria. The GA incorporates spatial and topological information by operating directly with a graph based representation. Initial results show this to be a promising technique for positioning graph nodes on a surface and may form the basis of a more general approach for problems involving multi-criteria spatial optimisation

PaL Diagrams: A Linear Diagram-Based Visual Language

Linear diagrams have recently been shown to be more effective than Euler diagrams when used for set-based reasoning. However, unlike the growing corpus of knowledge about formal aspects of Euler and Venn diagrams, there has been no formalisation of linear diagrams. To fill this knowledge gap, we present and formalise Point and Line (PaL) diagrams, an extension of simple linear diagrams containing points, thus providing a formal foundation for an effective visual language.We prove that PaL diagrams are exactly as expressive as monadic first-order logic with equality, gaining, as a corollary, an equivalence with the Euler diagram extension called spider diagrams. The method of proof provides translations between PaL diagrams and sentences of monadic first-order logic