Fast Edge-Routing for Large Graphs

Dwyer, Tim; Nachmanson, Lev

doi:10.1007/978-3-642-11805-0_15

Cited by 19 publications

(19 citation statements)

References 12 publications

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“…The bundling is achieved by clustering intersection points of the graph edges and Delaunay edges or by collapsing Delaunay edges. An even more adaptive approach is described by Dwyer and Nachmanson [7], where a visibility graph is used as a routing network.…”

Section: Related Workmentioning

confidence: 99%

Drawing Clustered Graphs as Topographic Maps

Gronemann

Jünger

2013

Graph Drawing

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Abstract. The visualization of clustered graphs is an essential tool for the analysis of networks, in particular, social networks, in which clustering techniques like community detection can reveal various structural properties. In this paper, we show how clustered graphs can be drawn as topographic maps, a type of map easily understandable by users not familiar with information visualization. Elevation levels of connected entities correspond to the nested structure of the cluster hierarchy. We present methods for initial node placement and describe a tree mapping based algorithm that produces an area efficient layout. Given this layout, a triangular irregular mesh is generated that is used to extract the elevation data for rendering the map. In addition, the mesh enables the routing of edges based on the topographic features of the map.

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Section: Related Workmentioning

confidence: 99%

Drawing Clustered Graphs as Topographic Maps

Gronemann

Jünger

2013

Graph Drawing

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“…Instead, an edge can be drawn via polyline, curve, etc. The majority of the edge routing algorithms tries to optimize certain predefined requirements for the route [Dwyer and Nachmanson 2009], such as minimizing a number of bends or maximizing the smallest bending angle. However, we need the graph layout as an input for constructing contours.…”

Section: Graph Drawingmentioning

confidence: 99%

Geometry-preserving topological landscapes

Beketayev

Weber

Morozov

et al. 2012

Proceedings of the Workshop at SIGGRAPH Asia

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We propose a novel technique for building geometry-preserving topological landscapes. Our technique creates a direct correlation between a scalar function and its topological landscape. This correlation is accomplished by introducing the notion of geometric proximity into the topological landscapes, reflecting the distance of topological features within the function domain. Furthermore, this technique enables direct comparative analysis between scalar functions, as long as they are defined on the same domain.We describe a construction technique that consists of three stages: contour tree computation, contour tree layout, and landscape construction. We provide a detailed description for the latter two steps. For the contour tree layout stage, we discuss dimension reduction and edge routing techniques that produce a drawing of the contour tree on the plane that preserves the geometric proximity. For the landscape construction stage, we develop a contour construction algorithm that takes the contour tree layout as an input, adds contours at heights that correspond to saddles of the contour tree, and produces a contour map. After an additional triangulation step, this construction method results in the landscape that has the same contour tree as the original function.

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“…The technique was ported to tangent visibility graphs by [24]. Finally, Dwyer and Nachmanson [11] give a fast heuristic to compute an approximation of the visibility graph to reduce the time complexity of the approach and therefore to support large graph edge routing. These approaches efficiently reduce edge clutter by avoiding node-edge overlaps, however they do not help the user to identify high-level edge patterns.…”

Section: Edge Clutter Reductionmentioning

confidence: 99%

“…[8,10,24,11]). Among theses techniques, one can find the confluent drawing method (e.g [8]) but also heuristics based on the visibility graph and shortest path edge routing (e.g [10,24,11]). These approaches efficiently reduce edge clutter by either reducing edge crossings or avoiding node-edge overlaps.…”

Section: Introductionmentioning

confidence: 99%