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30
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 34 (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.
TreePlus: Interactive Exploration of Networks with Enhanced Tree Layouts
 IEEE Transactions on Visualization and Computer Graphics
, 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 33 (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 than 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.
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 29 (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.
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 18 (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.
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 (1 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...
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 fast p ..."
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Cited by 14 (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.
Representing Space: A Hybrid Genetic Algorithm for Aesthetic Graph Layout
, 1998
"... This paper describes a hybrid Genetic Algorithm (GA) that is used to improve the layout of a graph according to a number of aesthetic criteria. The GA incorporates spatial and topological information by operating directly with a graph based representation. Initial results show this to be a promising ..."
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Cited by 8 (2 self)
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This paper describes a hybrid Genetic Algorithm (GA) that is used to improve the layout of a graph according to a number of aesthetic criteria. The GA incorporates spatial and topological information by operating directly with a graph based representation. Initial results show this to be a promising technique for positioning graph nodes on a surface and may form the basis of a more general approach for problems involving multicriteria spatial optimisation. 1. Introduction and Background Many spatial problems have a common need to locate interacting objects on a surface. Applications as diverse as geographical data analysis and molecular modelling deal with location as a special feature within a vector of attributes that describe a problem. Generic GAs have been used in applications such as electronic engineering design problems [6]; molecular conformational analysis [13,14,]; network and graph optimisation [15,17]. These systems deal with a variety of graph based representations but...
A New Approximation Algorithm for Finding Heavy Planar Subgraphs
 ALGORITHMICA
, 1997
"... We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NPHard problem of finding a heaviest planar subgraph in an edgeweighted graph G. This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM ..."
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Cited by 8 (2 self)
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We provide the first nontrivial approximation algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH, the NPHard problem of finding a heaviest planar subgraph in an edgeweighted graph G. This problem has applications in circuit layout, facility layout, and graph drawing. No previous algorithm for MAXIMUM WEIGHT PLANAR SUBGRAPH had performance ratio exceeding 1=3, which is obtained by any algorithm that produces a maximum weight spanning tree in G. Based on the BermanRamaiyer Steiner tree algorithm, the new algorithm has performance ratio at least 1/3 + 1/72. We also show that if G is complete and its edge weights satisfy the triangle inequality, then the performance ratio is at least 3/8. Furthermore, we derive the first nontrivial performance ratio (7/12 instead of 1/2) for the NPHard MAXIMUM WEIGHT OUTERPLANAR SUBGRAPH problem.