Improved Optimal and Approximate Power Graph Compression for Clearer Visualisation of Dense Graphs

Drawings of highly connected (dense) graphs can be very difficult to read. Power Graph Analysis offers an alternate way to draw a graph in which sets of nodes with common neighbours are shown grouped into modules. An edge connected to the module then implies a connection to each member of the module. Thus, the entire graph may be represented with much less clutter and without loss of detail. A recent experimental study has shown that such lossless compression of dense graphs makes it easier to follow paths. However, computing optimal power graphs is difficult. In this paper, we show that computing the optimal power-graph with only one module is NP-hard and therefore likely NP-hard in the general case. We give an ILP model for power graph computation and discuss why ILP and CP techniques are poorly suited to the problem. Instead, we are able to find optimal solutions much more quickly using a custom search method. We also show how to restrict this type of search to allow only limited back-tracking to provide a heuristic that has better speed and better results than previously known heuristics.Comment: Extended technical report accompanying the PacificVis 2013 paper of the same nam

Interactive, Constraint-based Layout of Engineering Diagrams

Many engineering disciplines require visualisation of networks. Constrained graph layout is a powerful new approach to network layout that allows the user to impose a wide variety application-specific placement constraints—such as downwards pointing directed edges, alignment of nodes, cluster containment and non-overlapping nodes and clusters—on the layout. We have recently developed an efficient algorithm for topology-preserving constrained graph layout. This underpins two dynamic graph layout applications we have developed: a network diagram authoring tool, Dunnart, and a network diagram browser. In this paper we provide an overview of topology-preserving constrained graph layout and illustrate how Dunnart and the network diagram browser can be applied to engineering diagram authoring and visualisation

Topographical and chemical effects of electrochemically assisted deposited hydroxyapatite coatings on osteoblast-like cells

A recently commercialised hydroxyapatite electrochemically assisted chemical deposition technique (BoneMaster) has been shown to induce increased bone apposition; whether this response is caused by the surface topography or chemistry is unknown. An in-vitro examination using human osteoblast-like cells was performed on a series of BoneMaster-coated surfaces. The chemistry was separated from the topography using a thin gold coating; Thermanox coverslips were used as a control. BoneMaster surfaces showed significantly greater alkaline phosphatase activity and osteocalcin production compared with controls; however, no difference was found between the gold-coated and uncoated BoneMaster samples, indicating topography is the main contributing factor