Improving Automated Layout Techniques for the Production of Schematic Diagrams

This thesis explores techniques for the automated production of schematic diagrams, in particular those in the style of metro maps. Metro map style schematics are used across the world, typically to depict public transport networks, and therefore benefit from an innate level of user familiarity not found with most other data visualisation styles. Currently, this style of schematic is used infrequently due to the difficulties involved with creating an effective layout – there are no software tools to aid with the positioning of nodes and other features, resulting in schematics being produced by hand at great expense of time and effort. Automated schematic layout has been an active area of research for the past decade, and part of our work extends upon an effective current technique – multi-criteria hill climbing. We have implemented additional layout criteria and clustering techniques, as well as performance optimisations to improve the final results. Additionally, we ran a series of layouts whilst varying algorithm parameters in an attempt to identify patterns specific to map characteristics. This layout algorithm has been implemented into a custom-written piece of software running on the Android operating system. The software is targeted at tablet devices, using their touch-sensitive screens with a gesture recognition system to allow users to construct complex schematics using sequences of simple gestures. Following on from this, we present our work on a modified force-directed layout method capable of producing fast, high-quality, angular schematic layouts. Our method produces superior results to the previous octilinear force-directed layout method, and is capable of producing results comparable to many of the much slower current approaches. Using our force-directed layout method we then implemented a novel mental map preservation technique which aims to preserve node proximity relations during optimisation; we believe this approach provides a number of benefits over the the more common method of preserving absolute node positions. Finally, we performed a user study on our method to test the effect of varying levels of mental map preservation on diagram comprehension

On Planar Polyline Drawings

We present a linear time algorithm that produces a planar polyline drawing for a plane graph with $n$ vertices in a grid of size bounded by $(p+1) times (n-2)$, where $p leq (lfloor frac2n-53rfloor)$. It uses at most $p leq lfloorfrac2n-53rfloor$ bends, and each edge uses at most one bend. Compared with the area optimal polyline drawing algorithm in [3], our algorithm uses a larger grid size bound in trade for a smaller bound on the total number of bends. Their bend bound is $(n-2)$. Our algorithm is based on a transformation from Schnyder's realizers [6, 7] of maximal plane graphs to transversal structures [4, 5] for maximal internally 4-connected plane graphs. This transformation reveals important relations between the two combinatorial structures for plane graphs, which is of independent interest