Results 1  10
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28
Simultaneous embedding of planar graphs with few bends
 In 12th Symposium on Graph Drawing (GD
, 2004
"... We consider several variations of the simultaneous embedding problem for planar graphs. We begin with a simple proof that not all pairs of planar graphs have simultaneous geometric embedding. However, using bends, pairs of planar graphs can be simultaneously embedded on the O(n 2) × O(n 2) grid, wit ..."
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Cited by 36 (7 self)
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We consider several variations of the simultaneous embedding problem for planar graphs. We begin with a simple proof that not all pairs of planar graphs have simultaneous geometric embedding. However, using bends, pairs of planar graphs can be simultaneously embedded on the O(n 2) × O(n 2) grid, with at most three bends per edge, where n is the number of vertices. The O(n) time algorithm guarantees that two corresponding vertices in the graphs are mapped to the same location in the final drawing and that both the drawings are crossingfree. The special case when both input graphs are trees has several applications, such as contour tree simplification and evolutionary biology. We show that if both the input graphs are are trees, only one bend per edge is required. The O(n) time algorithm guarantees that both drawings are crossingsfree, corresponding tree vertices are mapped to the same locations, and all vertices (and bends) are on the O(n 2) × O(n 2) grid (O(n 3) × O(n 3) grid). For the special case when one of the graphs is a tree and the other is a path we can find simultaneous embedding with fixededges. That is, we can guarantee that corresponding vertices are mapped to the same locations and that corresponding edges are drawn the same way. We describe an O(n) time algorithm for simultaneous embedding with fixededges for treepath pairs with at most one bend per treeedge and no bends along path edges, such that all vertices (and bends) are on the O(n) × O(n 2) grid, (O(n 2) × O(n 3) grid).
Simultaneous graph embeddings with fixed edges
 IN 32ND WORKSHOP ON GRAPHTHEORETIC CONCEPTS IN COMPUTER SCIENCE (WG
, 2006
"... We study the problem of simultaneously embedding several graphs on the same vertex set in such a way that edges common to two or more graphs are represented by the same curve. This problem is known as simultaneously embedding graphs with fixed edges. We show that this problem is closely related to ..."
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Cited by 18 (9 self)
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We study the problem of simultaneously embedding several graphs on the same vertex set in such a way that edges common to two or more graphs are represented by the same curve. This problem is known as simultaneously embedding graphs with fixed edges. We show that this problem is closely related to the weak realizability problem: Can a graph be drawn such that all edge crossings occur in a given set of edge pairs? By exploiting this relationship we can explain why the simultaneous embedding problem is challenging, both from a computational and a combinatorial point of view. More precisely, we prove that simultaneously embedding graphs with fixed edges is NPcomplete even for three planar graphs. For two planar graphs the complexity status is still open.
A Quantitative Comparison of StressMinimization Approaches for Offline Dynamic Graph Drawing
, 2012
"... In dynamic graph drawing, the input is a sequence of graphs for which a sequence of layouts is to be generated such that the quality of individual layouts is balanced with layout stability over time. Qualitatively different extensions of drawing algorithms for static graphs to the dynamic case have ..."
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Cited by 16 (2 self)
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In dynamic graph drawing, the input is a sequence of graphs for which a sequence of layouts is to be generated such that the quality of individual layouts is balanced with layout stability over time. Qualitatively different extensions of drawing algorithms for static graphs to the dynamic case have been proposed, but little is known about their relative utility. We report on a quantitative study comparing the three prototypical extensions via their adaptation for the stressminimization framework. While some findings are more subtle, the linking approach connecting consecutive instances of the same vertex is found to be the overall method of choice.
Visualization Methods for Longitudinal Social Networks and Actorbased Modeling
, 2011
"... As a consequence of the rising interest in longitudinal social networks and their analysis, there is also an increasing demand for tools to visualize them. We argue that similar adaptations of stateoftheart graphdrawing methods can be used to visualize longitudinal networks and the fit of actor ..."
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Cited by 11 (3 self)
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As a consequence of the rising interest in longitudinal social networks and their analysis, there is also an increasing demand for tools to visualize them. We argue that similar adaptations of stateoftheart graphdrawing methods can be used to visualize longitudinal networks and the fit of actorbased models, the most prominent approach for analyzing such networks. The proposed methods are illustrated on a longitudinal network of acquaintanceship among university freshmen.
Interactive Graph Matching and Visual Comparison of Graphs and Clustered Graphs
 In Proc. AVI, ACM (2012
"... We introduce interactive graph matching, a process that conciliates visualization, interaction and optimization approaches to address the graph matching and graph comparison problems as a whole. Interactive graph matching is based on a multilayered interaction model and on a visual reification of g ..."
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Cited by 10 (2 self)
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We introduce interactive graph matching, a process that conciliates visualization, interaction and optimization approaches to address the graph matching and graph comparison problems as a whole. Interactive graph matching is based on a multilayered interaction model and on a visual reification of graph matching functions. We present three case studies and a system named Donatien to demonstrate the interactive graph matching approach. The three case studies involve different datasets: a) subgraphs of a lexical network, b) graph of keywords extracted from the InfoVis contest benchmark, and c) clustered graphs computed from different clustering algorithms for comparison purposes.
An interactive multiuser system for simultaneous graph drawing
 In Proc. Intl. Symp. Graph Drawing
, 2004
"... Abstract. In this paper we consider the problem of simultaneous drawing of two graphs. The goal is to produce aesthetically pleasing drawings for the two graphs by means of a heuristic algorithm and with human assistance. Our implementation uses the DiamondTouch table, a multiuser, touchsensitive i ..."
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Cited by 9 (3 self)
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Abstract. In this paper we consider the problem of simultaneous drawing of two graphs. The goal is to produce aesthetically pleasing drawings for the two graphs by means of a heuristic algorithm and with human assistance. Our implementation uses the DiamondTouch table, a multiuser, touchsensitive input device, to take advantage of direct physical interaction of several users working collaboratively. The system can be downloaded at
Crossing minimization meets simultaneous drawing
 In IEEE Pacific Visualisation Symposium
, 2008
"... We define the concept of crossing numbers for simultaneous graphs by extending the crossing number problem of traditional graphs. We discuss differences to the traditional crossing number problem, and give an NPcompleteness proof and lower and upper bounds for the new problem. Furthermore, we show ..."
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Cited by 9 (2 self)
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We define the concept of crossing numbers for simultaneous graphs by extending the crossing number problem of traditional graphs. We discuss differences to the traditional crossing number problem, and give an NPcompleteness proof and lower and upper bounds for the new problem. Furthermore, we show how existing heuristic and exact algorithms for the traditional problem can be adapted to the new task of simultaneous crossing minimization, and report on a brief experimental study of their implementations.
Smooth bundling of large streaming and sequence graphs
 In Proc. PacificVis
, 2013
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 8 (5 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
TELEA A.: Bundled Visualization of Dynamic Graph and Trail Data
 IEEE Transactions on Visualization and Computer Graphics
, 2013
"... the Netherlands Abstract — Depicting change captured by dynamic graphs and temporal paths, or trails, is hard. We present two techniques for simplified visualization of such datasets using edge bundles. The first technique uses an efficient imagebased bundling method to create smoothly changing bun ..."
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Cited by 6 (2 self)
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the Netherlands Abstract — Depicting change captured by dynamic graphs and temporal paths, or trails, is hard. We present two techniques for simplified visualization of such datasets using edge bundles. The first technique uses an efficient imagebased bundling method to create smoothly changing bundles from streaming graphs. The second technique adds edgecorrespondence data atop of any static bundling algorithm, and is best suited for graph sequences. We show how these techniques can produce simplified visualizations of streaming and sequence graphs. Next, we show how several temporal attributes can be added atop of our dynamic graphs. We illustrate our techniques with datasets from aircraft monitoring, software engineering, and eyetracking of static and dynamic scenes. 1