Results 1  10
of
30
Circular Drawings of Rooted Trees
 IN REPORTS OF THE CENTRE FOR MATHEMATICS AND COMPUTER SCIENCES
, 1998
"... We describe an algorithm producing circular layouts for trees, that is drawings, where subtrees of a node lie within circles, and these circles are themselves placed on the circumference of a circle. The complexity and methodology of our algorithm compares to Reingold and Tilford's algorithm for ..."
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Cited by 19 (1 self)
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We describe an algorithm producing circular layouts for trees, that is drawings, where subtrees of a node lie within circles, and these circles are themselves placed on the circumference of a circle. The complexity and methodology of our algorithm compares to Reingold and Tilford's algorithm for trees [11]. Moreover, the algorithm naturally admits distortion transformations of the layout. This, added to its low complexity, makes it very well suited to be used in an interactive environment.
Proximity Constraints and Representable Trees
, 1995
"... This paper examines an infinite family of proximity drawings of graphs called open and closed fidrawings, first defined by Kirkpatrick and Radke [15, 21] in the context of computational morphology. Such proximity drawings include as special cases the wellknown Gabriel, relative neighborhood and ..."
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Cited by 19 (10 self)
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This paper examines an infinite family of proximity drawings of graphs called open and closed fidrawings, first defined by Kirkpatrick and Radke [15, 21] in the context of computational morphology. Such proximity drawings include as special cases the wellknown Gabriel, relative neighborhood and strip drawings. Complete characterizations of those trees that admit open fidrawings for 0 fi ! fi ! 1 or closed fidrawings for 0 fi ! fi 1 are given, as well as partial characterizations for other values of fi. For the intervals of fi in which complete characterizations are given, it can be determined in linear time whether a tree admits an open or closed fidrawing, and, if so, such a drawing can be computed in linear time in the real RAM model. Finally, a complete characterization of all graphs which admit closed strip drawings is given.
Radial Level Planarity Testing and Embedding in Linear Time
 Journal of Graph Algorithms and Applications
, 2005
"... A graph with a given partition of the vertices on k concentric circles is radial level planar if there is a vertex permutation such that the edges can be routed strictly outwards without crossings. Radial level planarity extends level planarity, where the vertices are placed on k horizontal lines an ..."
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Cited by 19 (9 self)
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A graph with a given partition of the vertices on k concentric circles is radial level planar if there is a vertex permutation such that the edges can be routed strictly outwards without crossings. Radial level planarity extends level planarity, where the vertices are placed on k horizontal lines and the edges are routed strictly downwards without crossings. The extension is characterised by rings, which are level nonplanar biconnected components. Our main results are linear time algorithms for radial level planarity testing and for computing an embedding. We introduce PQRtrees as a new data structure where Rnodes and associated templates for their manipulation are introduced to deal with rings. Our algorithms extend level planarity testing and embedding algorithms which use PQtrees.
Visual comparison of hierarchically organized data
 Comput. Graph. Forum
"... We provide a novel visualization method for the comparison of hierarchically organized data. Our technique visualizes a pair of hierarchies that are to be compared and simultaneously depicts how these hierarchies are related by explicitly visualizing the relations between matching subhierarchies. El ..."
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Cited by 16 (1 self)
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We provide a novel visualization method for the comparison of hierarchically organized data. Our technique visualizes a pair of hierarchies that are to be compared and simultaneously depicts how these hierarchies are related by explicitly visualizing the relations between matching subhierarchies. Elements that are unique to each hierarchy are shown, as well as the way in which hierarchy elements are relocated, split or joined. The relations between hierarchy elements are visualized using Hierarchical Edge Bundles (HEBs). HEBs reduce visual clutter, they visually emphasize the aforementioned splits, joins, and relocations of subhierarchies, and they provide an intuitive way in which users can interact with the relations. The focus throughout this paper is on the comparison of different versions of hierarchically organized software systems, but the technique is applicable to other kinds of hierarchical data as well. Various data sets of actual software systems are used to show how our technique can be employed to easily spot splits, joins, and relocations of elements, how sorting both hierarchies with respect to each other facilitates comparison tasks, and how user interaction is supported. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Viewing Algorithms I.3 1
Animated Exploration of Graphs with Radial Layout
 Proc. of Information Visualization 2001
, 2001
"... We describe a new animation technique for supporting interactive exploration of a graph, building on the wellknown radial tree layout method. When a node is selected to become the center of interest, our visualization performs an animated transition to a new layout. Our approach is to linearly inter ..."
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Cited by 13 (0 self)
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We describe a new animation technique for supporting interactive exploration of a graph, building on the wellknown radial tree layout method. When a node is selected to become the center of interest, our visualization performs an animated transition to a new layout. Our approach is to linearly interpolate the polar coordinates of the nodes, while enforcing constraints on the layout to keep the transition easy to follow. We apply this technique to visualizations of social networks and of the Gnutella filesharing network, and discuss our findings and usability results. Key Words: graph drawing, animation, interaction 1.
Latour  a Tree Visualisation System
 In Proceedings of the Symposium on Graph Drawing ’99
, 1999
"... This paper presents some of the most important features of a tree visualisation system called Latour, developed for the purposes of information visualisation. This system includes a number of interesting and unique characteristics, for example the provision for visual cues based on complexity metric ..."
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Cited by 11 (0 self)
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This paper presents some of the most important features of a tree visualisation system called Latour, developed for the purposes of information visualisation. This system includes a number of interesting and unique characteristics, for example the provision for visual cues based on complexity metrics on graphs, which represent general principles that, in our view, graph based information visualisation systems should generally offer.
On Balloon Drawings of Rooted Trees
 Proc. 13th International Symposium on Graph Drawing (GD’05
, 2005
"... Among various styles of tree drawing reported in the literature, balloon drawing enjoys a desirable feature of displaying tree structures in a rather balanced fashion. Each subtree in the balloon drawing of a tree is enclosed in a circle. Along any path from the root node, the radius of each circle ..."
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Cited by 6 (0 self)
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Among various styles of tree drawing reported in the literature, balloon drawing enjoys a desirable feature of displaying tree structures in a rather balanced fashion. Each subtree in the balloon drawing of a tree is enclosed in a circle. Along any path from the root node, the radius of each circle reflects the number of descendants associated with the root node of the subtree. In this paper, we investigate various issues related to balloon drawings of rooted trees from the algorithmic viewpoint. First, we design an efficient algorithm to optimize the angular resolution and the aspect ratio for the balloon drawings of rooted unordered trees. For the case of ordered trees for which the center of the enclosing circle of a subtree need not coincide with the root of the subtree, flipping the drawing of a subtree (along the axis from the parent to the root of the subtree) might change both the aspect ratio and the angular resolution of the drawing. We show that optimizing the angular resolution as well as the aspect ratio with respect to this type of rooted ordered trees is reducible to the perfect matching problem for bipartite graphs, which is solvable in polynomial time. In addition, a related problem concerning the optimization of the drawing area can be modelled as a specific type of nonlinear programming for which there exist several robust algorithms in practice. With a slight modification to the balloon drawing, we are able to generate the drawings of galaxy systems, Htrees, and sparse graphs, which are of practical interest.
Radial coordinate assignment for level graphs
 Proc. Computing and Combinatorics, COCOON 2005, volume 3595 of LNCS
, 2005
"... Abstract. We present a simple linear time algorithm for drawing level graphs with a given ordering of the vertices within each level. The algorithm draws in a radial fashion without changing the vertex ordering, and therefore without introducing new edge crossings. Edges are drawn as sequences of sp ..."
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Cited by 6 (3 self)
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Abstract. We present a simple linear time algorithm for drawing level graphs with a given ordering of the vertices within each level. The algorithm draws in a radial fashion without changing the vertex ordering, and therefore without introducing new edge crossings. Edges are drawn as sequences of spiral segments with at most two bends. 1
Effects of Sociogram Drawing Conventions and Edge Crossings in Social Network Visualization
 Journal of Graph Algorithms and Applications
, 2007
"... This paper describes a withinsubjects experiment. In this experiment, the effects of different spatial layouts on human sociogram perception are examined. We compare the relative effectiveness of five sociogram drawing conventions in communicating underlying network substance, based on user task pe ..."
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Cited by 6 (0 self)
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This paper describes a withinsubjects experiment. In this experiment, the effects of different spatial layouts on human sociogram perception are examined. We compare the relative effectiveness of five sociogram drawing conventions in communicating underlying network substance, based on user task performance and personal preference. We also explore the impact of edge crossings, a widely accepted readability aesthetic. Both objective performance and subjective questionnaire measures are employed in the study. Subjective data are gathered based on the methodology of Purchase et al. [70], while objective data are collected through an online system. We found that 1) both edge crossings and drawing conventions pose significant effects on user preference and task performance of finding groups, but neither has much impact on the perception of actor status. On the other hand, node positioning and angular resolution may be more important in perceiving actor status. In visualizing social networks, it is important to note that the techniques that are highly preferred by users do not necessarily lead to best task performance. 2) subjects have a strong preference of placing nodes on the top or in the center to highlight importance, and clustering nodes in the same group and separating clusters to highlight groups. They have tendency to believe that nodes on the top or in the center are more important, and nodes in close proximity belong to the same group. Some preliminary recommendations for sociogram design and hypotheses about human reading behavior are proposed.
Drawing Trees with Perfect Angular Resolution and Polynomial Area
"... Abstract. We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex, v, equal to 2π/d(v). We show: 1. Any unordered tree has a crossingfree straightline drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require e ..."
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Cited by 6 (6 self)
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Abstract. We study methods for drawing trees with perfect angular resolution, i.e., with angles at each vertex, v, equal to 2π/d(v). We show: 1. Any unordered tree has a crossingfree straightline drawing with perfect angular resolution and polynomial area. 2. There are ordered trees that require exponential area for any crossingfree straightline drawing having perfect angular resolution. 3. Any ordered tree has a crossingfree Lombardistyle drawing (where each edge is represented by a circular arc) with perfect angular resolution and polynomial area. Thus, our results explore what is achievable with straightline drawings and what more is achievable with Lombardistyle drawings, with respect to drawings of trees with perfect angular resolution. 1