26 research outputs found
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