Edge Routing with Ordered Bundles

Edge bundling reduces the visual clutter in a drawing of a graph by uniting the edges into bundles. We propose a method of edge bundling drawing each edge of a bundle separately as in metro-maps and call our method ordered bundles. To produce aesthetically looking edge routes it minimizes a cost function on the edges. The cost function depends on the ink, required to draw the edges, the edge lengths, widths and separations. The cost also penalizes for too many edges passing through narrow channels by using the constrained Delaunay triangulation. The method avoids unnecessary edge-node and edge-edge crossings. To draw edges with the minimal number of crossings and separately within the same bundle we develop an efficient algorithm solving a variant of the metro-line crossing minimization problem. In general, the method creates clear and smooth edge routes giving an overview of the global graph structure, while still drawing each edge separately and thus enabling local analysis

GraphMaps: Browsing Large Graphs as Interactive Maps

Algorithms for laying out large graphs have seen significant progress in the past decade. However, browsing large graphs remains a challenge. Rendering thousands of graphical elements at once often results in a cluttered image, and navigating these elements naively can cause disorientation. To address this challenge we propose a method called GraphMaps, mimicking the browsing experience of online geographic maps. GraphMaps creates a sequence of layers, where each layer refines the previous one. During graph browsing, GraphMaps chooses the layer corresponding to the zoom level, and renders only those entities of the layer that intersect the current viewport. The result is that, regardless of the graph size, the number of entities rendered at each view does not exceed a predefined threshold, yet all graph elements can be explored by the standard zoom and pan operations. GraphMaps preprocesses a graph in such a way that during browsing, the geometry of the entities is stable, and the viewer is responsive. Our case studies indicate that GraphMaps is useful in gaining an overview of a large graph, and also in exploring a graph on a finer level of detail.Comment: submitted to GD 201

Play to Test

Testing tasks can be viewed (and organized!) as games against nature. We study reachability games in the context of testing. Such games are ubiquitous. A single industrial test suite may involve many instances of a reachability game. Hence the importance of optimal or near optimal strategies for reachability games. One can use linear programming or the value iteration method of Markov decision process theory to find optimal strategies. Both methods have been implemented in an industrial model-based testing tool, Spec Explorer, developed at Microsoft Research

Spherical similarity explorer for comparative case analysis

Comparative Case Analysis (CCA) is an important tool for criminal investigation and crime theory extraction. It analyzes the commonalities and differences between a collection of crime reports in order to understand crime patterns and identify abnormal cases. A big challenge of CCA is the data processing and exploration. Traditional manual approach can no longer cope with the increasing volume and complexity of the data. In this paper we introduce a novel visual analytics system, Spherical Similarity Explorer (SSE) that automates the data processing process and provides interactive visualizations to support the data exploration. We illustrate the use of the system with uses cases that involve real world application data and evaluate the system with criminal intelligence analysts

Test Model Coverage Analysis under Uncertainty

In model-based testing (MBT) we may have to deal with a non-deterministic model, e.g. because abstraction was applied, or because the software under test itself is non-deterministic. The same test case may then trigger multiple possible execution paths, depending on some internal decisions made by the software. Consequently, performing precise test analyses, e.g. to calculate the test coverage, are not possible. This can be mitigated if developers can annotate the model with estimated probabilities for taking each transition. A probabilistic model checking algorithm can subsequently be used to do simple probabilistic coverage analysis. However, in practice developers often want to know what the achieved aggregate coverage, which unfortunately cannot be re-expressed as a standard model checking problem. This paper presents an extension to allow efficient calculation of probabilistic aggregate coverage, and moreover also in combination with k-wise coverage

Drawing graphs with glee

Abstract. This paper describes novel methods we developed to lay out graphs using Sugiyama’s scheme [16] in a tool named GLEE. The main contributions are: a heuristic for creating a graph layout with a given aspect ratio, an efficient method of edge-crossings counting while performing adjacent vertex swaps, and a simple and fast spline routing algorithm.

Graph Drawing Contest Report

This report describes the 21st Annual Graph Drawing Contest, held in conjunction with the 2014 Graph Drawing Symposium in Würzburg, Germany. The purpose of the contest is to monitor and challenge the current state of graph-drawing technology

Improving Layered Graph Layouts with Edge Bundling

We show how to improve the Sugiyama scheme by edge bundling. Our method modifies the layout produced by the Sugiyama scheme by bundling some of the edges together. The bundles are created by a new algorithm based on minimizing the total ink needed to draw the graph edges. We give several implementations that vary in quality of the resulting layout and execution time. To diminish the number of edge crossings inside of the bundles we apply a metro-line crossing minimization technique. The method preserves the Sugiyama style of the layout and creates a more readable view of the graph