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Hierarchical edge bundles: Visualization of adjacency relations in hierarchical data
 IEEE Transactions on Visualization and Computer Graphics
, 2006
"... Abstract—A compound graph is a frequently encountered type of data set. Relations are given between items, and a hierarchy is defined on the items as well. We present a new method for visualizing such compound graphs. Our approach is based on visually bundling the adjacency edges, i.e., nonhierarch ..."
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Cited by 151 (9 self)
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Abstract—A compound graph is a frequently encountered type of data set. Relations are given between items, and a hierarchy is defined on the items as well. We present a new method for visualizing such compound graphs. Our approach is based on visually bundling the adjacency edges, i.e., nonhierarchical edges, together. We realize this as follows. We assume that the hierarchy is shown via a standard tree visualization method. Next, we bend each adjacency edge, modeled as a Bspline curve, toward the polyline defined by the path via the inclusion edges from one node to another. This hierarchical bundling reduces visual clutter and also visualizes implicit adjacency edges between parent nodes that are the result of explicit adjacency edges between their respective child nodes. Furthermore, hierarchical edge bundling is a generic method which can be used in conjunction with existing tree visualization techniques. We illustrate our technique by providing example visualizations and discuss the results based on an informal evaluation provided by potential users of such visualizations.
Train tracks and confluent drawings
 In Graph Drawing (Proc. GD
, 2004
"... Abstract. Confluent graphs capture the connection properties of train tracks, offering a very natural generalization of planar graphs, and—as the example of railroad maps shows—are an important tool in graph visualization. In this paper we continue the study of confluent graphs, introducing strongly ..."
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Cited by 5 (0 self)
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Abstract. Confluent graphs capture the connection properties of train tracks, offering a very natural generalization of planar graphs, and—as the example of railroad maps shows—are an important tool in graph visualization. In this paper we continue the study of confluent graphs, introducing strongly confluent graphs and treeconfluent graphs. We show that strongly confluent graphs can be recognized in NP (the complexity of recognizing confluent graphs remains open). We also give a natural elimination ordering characterization of treeconfluent graphs, and we show that this class coincides with the (6, 2)chordal bipartite graphs. Finally, we define outerconfluent graphs and identify the bipartite permutation graphs as a natural subclass.
Forcedirected Lombardistyle graph drawing
 IN: PROC. 19TH INT. SYMP. ON GRAPH DRAWING
, 2011
"... A Lombardi drawing of a graph is defined as one in which vertices are represented as points, edges are represented as circular arcs between their endpoints, and every vertex has perfect angular resolution (angles between consecutive edges, as measured by the tangents to the circular arcs at the ve ..."
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Cited by 4 (2 self)
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A Lombardi drawing of a graph is defined as one in which vertices are represented as points, edges are represented as circular arcs between their endpoints, and every vertex has perfect angular resolution (angles between consecutive edges, as measured by the tangents to the circular arcs at the vertex, all have the same degree). We describe two algorithms that create “Lombardistyle” drawings (which we also call nearLombardi drawings), in which all edges are still circular arcs, but some vertices may not have perfect angular resolution. Both of these algorithms take a forcedirected, springembedding approach, with one using forces at edge tangents to produce curved edges and the other using dummy vertices on edges for this purpose. As we show, these approaches both produce nearLombardi drawings, with one being slightly better at achieving nearperfect angular resolution and the other being slightly better at balancing vertex placements.
UprightQuad Drawing of stPlanar Learning Spaces
, 2008
"... We consider graph drawing algorithms for learning spaces, a type of storiented partial cube derived from an antimatroid and used to model states of knowledge of students. We show how to draw any stplanar learning space so all internal faces are convex quadrilaterals with the bottom side horizontal ..."
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Cited by 3 (0 self)
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We consider graph drawing algorithms for learning spaces, a type of storiented partial cube derived from an antimatroid and used to model states of knowledge of students. We show how to draw any stplanar learning space so all internal faces are convex quadrilaterals with the bottom side horizontal and the left side vertical, with one minimal and one maximal vertex. Conversely, every such drawing represents an stplanar learning space. We also describe connections between these graphs and arrangements of translates of a quadrant. Our results imply that an antimatroid has order dimension two if and only if it has convex dimension two.
Dynamic distance hereditary graphs using split decomposition
 In Algorithms and Computation, 18th International Symposium (ISAAC
, 2007
"... Abstract. The problem of maintaining a representation of a dynamic graph as long as a certain property is satisfied has recently been considered for a number of properties. This paper presents an optimal algorithm for this problem on vertexdynamic connected distance hereditary graphs: both vertex i ..."
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Cited by 3 (1 self)
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Abstract. The problem of maintaining a representation of a dynamic graph as long as a certain property is satisfied has recently been considered for a number of properties. This paper presents an optimal algorithm for this problem on vertexdynamic connected distance hereditary graphs: both vertex insertion and deletion have complexity O(d), where d is the degree of the vertex involved in the modification. Our vertexdynamic algorithm is competitive with the existing linear time recognition algorithms of distance hereditary graphs, and is also simpler. Besides, we get a constant time edgedynamic recognition algorithm. To achieve this, we revisit the split decomposition by introducing graphlabelled trees. Doing so, we are also able to derive an intersection model for distance hereditary graphs, which answers an open problem. 1
Split Decomposition and graphlabelled trees: Characterizations and FullyDynamic Algorithms for Totally Decomposable Graphs
, 2008
"... In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two nontrivial subclasses, namely the cographs and the 3leaf power graphs. Precisely, w ..."
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In this paper, we revisit the split decomposition of graphs and give new combinatorial and algorithmic results for the class of totally decomposable graphs, also known as the distance hereditary graphs, and for two nontrivial subclasses, namely the cographs and the 3leaf power graphs. Precisely, we give strutural and incremental characterizations, leading to optimal fullydynamic recognition algorithms for vertex and edge modifications, for each of these classes. These results rely on a new framework to represent the split decomposition, namely the graphlabelled trees, which also captures the modular decomposition of graphs and thereby unify these two decompositions techniques. The point of the paper is to use bijections between these graph classes and trees whose nodes are labelled by cliques and stars. Doing so, we are also able to derive an intersection model for distance hereditary graphs, which answers an open problem.
Regular paper Communicated by:
, 2013
"... We show that a transitively reduced digraph has a confluent upward drawing if and only if its reachability relation has order dimension at most two. In this case, we construct a confluent upward drawing with O(n2) features, in an O(n)×O(n) grid in O(n2) time. For the digraphs representing seriespar ..."
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We show that a transitively reduced digraph has a confluent upward drawing if and only if its reachability relation has order dimension at most two. In this case, we construct a confluent upward drawing with O(n2) features, in an O(n)×O(n) grid in O(n2) time. For the digraphs representing seriesparallel partial orders we show how to construct a drawing with O(n) features in an O(n)×O(n) grid in O(n) time from a seriesparallel decomposition of the partial order. Our drawings are optimal in the number of confluent junctions they use. Submitted: