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46
Treeplus: Interactive exploration of networks with enhanced tree layouts
 IEEE TVCG
, 2006
"... Abstract—Despite extensive research, it is still difficult to produce effective interactive layouts for large graphs. Dense layout and occlusion make food webs, ontologies, and social networks difficult to understand and interact with. We propose a new interactive Visual Analytics component called T ..."
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Cited by 36 (4 self)
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Abstract—Despite extensive research, it is still difficult to produce effective interactive layouts for large graphs. Dense layout and occlusion make food webs, ontologies, and social networks difficult to understand and interact with. We propose a new interactive Visual Analytics component called TreePlus that is based on a treestyle layout. TreePlus reveals the missing graph structure with visualization and interaction while maintaining good readability. To support exploration of the local structure of the graph and gathering of information from the extensive reading of labels, we use a guiding metaphor of “Plant a seed and watch it grow. ” It allows users to start with a node and expand the graph as needed, which complements the classic overview techniques that can be effective at (but often limited to) revealing clusters. We describe our design goals, describe the interface, and report on a controlled user study with 28 participants comparing TreePlus with a traditional graph interface for six tasks. In general, the advantage of TreePlus over the traditional interface increased as the density of the displayed data increased. Participants also reported higher levels of confidence in their answers with TreePlus and most of them preferred TreePlus.
Optimal upward planarity testing of singlesource digraphs
 SIAM Journal on Computing
, 1998
"... Abstract. A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in softwar ..."
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Cited by 35 (4 self)
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Abstract. A digraph is upward planar if it has a planar drawing such that all the edges are monotone with respect to the vertical direction. Testing upward planarity and constructing upward planar drawings is important for displaying hierarchical network structures, which frequently arise in software engineering, project management, and visual languages. In this paper we investigate upward planarity testing of singlesource digraphs; we provide a new combinatorial characterization of upward planarity and give an optimal algorithm for upward planarity testing. Our algorithm tests whether a singlesource digraph with n vertices is upward planar in O(n) sequential time, and in O(log n) time on a CRCW PRAM with n log log n / log n processors, using O(n) space. The algorithm also constructs an upward planar drawing if the test is successful. The previously known best result is an O(n2)time algorithm by Hutton and Lubiw [Proc. 2nd ACM–SIAM Symposium on Discrete Algorithms, SIAM, Philadelphia, 1991, pp. 203–211]. No efficient parallel algorithms for upward planarity testing were previously known.
An Interactive ConstraintBased System for Drawing Graphs
 In Proceedings of UIST
, 1997
"... The GLIDE system is an interactive constraintbased editor for drawing small and mediumsized graphs (50 nodes or fewer) that organizes the interaction in a more collaborative manner than in previous systems. Its distinguishing features are a vocabulary of specialized constraints for graph drawing, ..."
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Cited by 31 (3 self)
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The GLIDE system is an interactive constraintbased editor for drawing small and mediumsized graphs (50 nodes or fewer) that organizes the interaction in a more collaborative manner than in previous systems. Its distinguishing features are a vocabulary of specialized constraints for graph drawing, and a simple constraintsatisfaction mechanism that allows the user to manipulate the drawing while the constraints are active. These features result in a graphdrawing editor that is superior in many ways to those based on more general and powerful constraintsatisfaction methods.
Constrained Higher Order Delaunay Triangulations
 COMPUT. GEOM. THEORY APPL
, 2004
"... We extend the notion of higherorder Delaunay triangulations to constrained higherorder Delaunay triangulations and provide various results. We can determine the order k of a given triangulation in O(min(nk log n log k, n n)) time. We show that the completion of a set of useful orderk Dela ..."
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Cited by 25 (8 self)
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We extend the notion of higherorder Delaunay triangulations to constrained higherorder Delaunay triangulations and provide various results. We can determine the order k of a given triangulation in O(min(nk log n log k, n n)) time. We show that the completion of a set of useful orderk Delaunay edges may have order 2k 2, which is worstcase optimal. We give an algorithm for the lowestorder completion for a set of useful orderk Delaunay edges when k 3. For higher orders the problem is open.
The Techniques of Komolgorov and Bardzin for Three Dimensional Orthogonal Graph Drawings
, 1995
"... This paper appears as Technical Report 9507, Department of Computer Science, University of Newcastle, Newcastle NSW 2308 Australia. ..."
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Cited by 20 (1 self)
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This paper appears as Technical Report 9507, Department of Computer Science, University of Newcastle, Newcastle NSW 2308 Australia.
An Algorithm For Drawing A Hierarchical Graph
, 1995
"... this paper we present a method for drawing "hierarchical directed graphs", which are digraphs in which each node is assigned a layer, as in Figure 1. ..."
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Cited by 18 (7 self)
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this paper we present a method for drawing "hierarchical directed graphs", which are digraphs in which each node is assigned a layer, as in Figure 1.
Linear area upward drawings of AVL trees
 COMPUTATIONAL GEOMETRY
, 1998
"... We prove that any AVL tree admits a lineararea straightline strictlyupward planar grid drawing, that is, a drawing in which (a) each edge is mapped into a single straightline segment, (b) each node is placed below its parent, (c) no two edges intersect, and (d) each node is mapped into a point w ..."
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Cited by 16 (1 self)
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We prove that any AVL tree admits a lineararea straightline strictlyupward planar grid drawing, that is, a drawing in which (a) each edge is mapped into a single straightline segment, (b) each node is placed below its parent, (c) no two edges intersect, and (d) each node is mapped into a point with integer coordinates.
Nonlinear Dimensionality Reduction of Data Manifolds With Essential Loops
, 2005
"... Numerous methods or algorithms have been designed to solve the problem of nonlinear dimensionality reduction (NLDR). However, very few among them are able to embed efficiently `circular' manifolds like cylinders or tori, which have one or more essential loops. This paper presents a simple and f ..."
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Cited by 15 (3 self)
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Numerous methods or algorithms have been designed to solve the problem of nonlinear dimensionality reduction (NLDR). However, very few among them are able to embed efficiently `circular' manifolds like cylinders or tori, which have one or more essential loops. This paper presents a simple and fast procedure that can tear or cut those manifolds, i.e. break their essential loops, in order to make their embedding in a lowdimensional space easier. The key idea is the following: starting from the available data points, the tearing procedure represents the underlying manifold by a graph and then builds a maximum subgraph with no loops anymore. Because it works with a graph, the procedure can preprocess data for all NLDR techniques that uses the same representation. Recent techniques using geodesic distances (Isomap, geodesic Sammon's mapping, geodesic CCA, etc.) or $K$ary neighborhoods (LLE, hLLE, Laplacian eigenmaps) fall in that category. After describing the tearing procedure in details, the paper comments a few experimental results.
Upward Planar Drawing of Single Source Acyclic Digraphs
, 1990
"... A upward plane drawing of a directed acyclic graph is a straight line drawing in the Euclidean plane such that all directed arcs point upwards. Thomassen [30] has given a nonalgorithmic, graphtheoretic characterization of those directed graphs with a single source that admit an upward drawing. We ..."
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Cited by 15 (0 self)
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A upward plane drawing of a directed acyclic graph is a straight line drawing in the Euclidean plane such that all directed arcs point upwards. Thomassen [30] has given a nonalgorithmic, graphtheoretic characterization of those directed graphs with a single source that admit an upward drawing. We present an efficient algorithm to test whether a given singlesource acyclic digraph has a plane upward drawing and, if so, to find a representation of one such drawing. The algorithm decomposes the graph into biconnected and triconnected components, and defines conditions for merging the components into an upward drawing of the original graph. For the triconnected components we provide a linear algorithm to test whether a given plane representation admits an upward drawing with the same faces and outer face, which also gives a simpler (and algorithmic) proof of Thomassen's result. The entire testing algorithm (for general single source directed acyclic graphs) operates in O(n²) time and...