Results 1  10
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18
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 26 (6 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
"... Foundation (JU204/101). Abstract. 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 t ..."
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Cited by 13 (7 self)
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Foundation (JU204/101). Abstract. 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. 1
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
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 8 (1 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.
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 7 (3 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.
A system for visualizing and analyzing the evolution of the Web with a time series of graphs
 In International workshop on automatic faceand gesturerecognition
, 2005
"... We propose WebRelievo, a system for visualizing and analyzing the evolution of the web structure based on a large Web archive with a series of snapshots. It visualizes the evolution with a time series of graphs, in which nodes are web pages, and edges are relationships between pages. Graphs can be c ..."
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Cited by 4 (0 self)
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We propose WebRelievo, a system for visualizing and analyzing the evolution of the web structure based on a large Web archive with a series of snapshots. It visualizes the evolution with a time series of graphs, in which nodes are web pages, and edges are relationships between pages. Graphs can be clustered to show the overview of changes in graphs. WebRelievo aligns these graphs according to their time, and automatically determines their layout keeping positions of nodes synchronized over time, so that the user can keep track pages and clusters. This visualization enables us to understand when pages appeared, how their relationships have evolved, and how clusters are merged and split over time. Current implementation of WebRelievo is based on six Japanese web archives crawled from 1999 to 2003. The user can interactively browse those graphs by changing the focused page and by changing layouts of graphs. Using WebRelievo we can answer historical questions, and to investigate changes in trends on the Web. We show the feasibility of WebRelievo by applying it to tracking trends in P2P systems and search engines for mobile phones, and to investigating link spamming.
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 4 (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 3 (0 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.
Interactively Visualizing Dynamic Social Networks with
"... The dynamic social network visualizer “DySoN ” (Dynamic Social Networks) aims at understanding patterns and structural changes in dynamic social networks that evolve over time via an interactive visualization approach. As an alternative and supplementation to the numerous other approaches to visuali ..."
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Cited by 2 (0 self)
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The dynamic social network visualizer “DySoN ” (Dynamic Social Networks) aims at understanding patterns and structural changes in dynamic social networks that evolve over time via an interactive visualization approach. As an alternative and supplementation to the numerous other approaches to visualization of social network data and as an attempt to overcome some of the drawbacks of these approaches, DySoN interactively visualizes streaming event data of social interactions by an interactive threedimensional model of interpolated NURBS ”tubes”, representing activity and social proximity within a given set of actors during a given time period by using three dimensions of temporal information mapping: spatial density (tube distance), tubecolor and tubediameter. We use a self assembled large collaboration network of Jazz musicians with a straightforward semantics for the computation of relation strengths for the evaluation of the approach. We also discuss applications of the concept for awareness services in mobile peer to peer social networks, which exhibit a vivid measurable social micro dynamics in time and space.
Visual Analysis of OnetoMany Matched Graphs
, 2010
"... Motivated by applications of social network analysis and of Web search clustering engines, we describe an algorithm and a system for the display and the visual analysis of two graphs G1 and G2 such that each Gi is defined on a different data set with its own primary relationships and there are secon ..."
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Cited by 2 (0 self)
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Motivated by applications of social network analysis and of Web search clustering engines, we describe an algorithm and a system for the display and the visual analysis of two graphs G1 and G2 such that each Gi is defined on a different data set with its own primary relationships and there are secondary relationships between the vertices of G1 and those of G2. Our main goal is to compute a drawing of G1 and G2 that makes clearly visible the relations between the two graphs by avoiding their crossings, and that also takes into account some other important aesthetic requirements like number of bends, area, and aspect ratio. Application examples and experiments on the system performances are also presented.