Results 1  10
of
18
ThreeDimensional Orthogonal Graph Drawing
, 2000
"... vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . ..."
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Cited by 27 (10 self)
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vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv I Orthogonal Graph Drawing 1 1
Drawing planar graphs symmetrically, III: Oneconnected planar graphs
 ALGORITHMICA
, 2006
"... Symmetry is one of the most important aesthetic criteria in graph drawing because it reveals structure in the graph. This paper discusses symmetric drawings of oneconnected planar graphs. More specifically, we discuss planar (geometric) automorphisms, that is, automorphisms of a graph G that can b ..."
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Cited by 8 (5 self)
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Symmetry is one of the most important aesthetic criteria in graph drawing because it reveals structure in the graph. This paper discusses symmetric drawings of oneconnected planar graphs. More specifically, we discuss planar (geometric) automorphisms, that is, automorphisms of a graph G that can be represented as symmetries of a planar drawing of G. Finding planar automorphisms is the first and most difficult step in constructing planar symmetric drawings of graphs. The problem of determining whether a given graph has a nontrivial geometric automorphism is NPcomplete for general graphs. The two previous papers in this series have discussed the problem of drawing planar graphs with a maximum number of symmetries, for the restricted cases where the graph is triconnected and biconnected. This paper extends the previous results to cover planar graphs that are oneconnected. We present a linear time algorithm for drawing oneconnected planar graphs with a maximum number of symmetries.
On Maximum Symmetric Subgraphs
 Proc. of Graph Drawing 2000, Lecture Notes in Computer Science
, 2001
"... Let G be an nnode graph. We address the problem of computing a maximum symmetric graph H from G by deleting nodes, deleting edges, and contracting edges. This NPcomplete problem arises naturally from the objective of drawing G as symmetrically as possible. We show that its tractability for the spe ..."
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Cited by 7 (1 self)
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Let G be an nnode graph. We address the problem of computing a maximum symmetric graph H from G by deleting nodes, deleting edges, and contracting edges. This NPcomplete problem arises naturally from the objective of drawing G as symmetrically as possible. We show that its tractability for the special cases of G being a plane graph, an ordered tree, and an unordered tree, depends on the type of operations used to obtain H from G. Moreover, we give an O(log n)approximation algorithm for the intractable case that H is obtained from a tree G by contracting edges. As a byproduct, we give an O(log n)approximation algorithm for an NPcomplete editdistance problem.
A new forcedirected graph drawing method based on edgeedge repulsion
 IN PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON INFORMATION VIZUALISATION (IV
, 2005
"... The conventional forcedirected methods for drawing undirected graphs are based on either vertexvertex repulsion or vertexedge repulsion. In this paper, we propose a new forcedirected method based on edgeedge repulsion to draw graphs. In our framework, edges are modelled as charged springs, and ..."
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Cited by 6 (0 self)
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The conventional forcedirected methods for drawing undirected graphs are based on either vertexvertex repulsion or vertexedge repulsion. In this paper, we propose a new forcedirected method based on edgeedge repulsion to draw graphs. In our framework, edges are modelled as charged springs, and a final drawing can be generated by adjusting positions of vertices according to spring forces and the repulsive forces, derived from potential fields, among edges. Different from the previous methods, our new framework has the advantage of overcoming the problem of zero angular resolution, guaranteeing the absence of any overlapping of edges incident to the common vertex. Given graph layouts probably generated by classical algorithms as the inputs to our algorithm, experimental results reveal that our approach produces promising drawings (especially for trees and hypercubes) not only preserving the original properties of a high degree of symmetry and uniform edge length, but also preventing zero angular resolution. By allowing vertexvertex overlapping, our algorithm also results in more symmetrical drawings. Furthermore, we apply the model to producing dynamical balloon view drawings of rooted trees, usually used in information visualization.
Crossing Minimization for Symmetries
 Proc. of ISAAC 2002, Lecture Notes in Computer Science
, 2002
"... We consider the problem of drawing a graph with a given symmetry such that the number of edge crossings is minimal. We show that this problem is NPhard, even if the order of orbits around the rotation center or along the reection axis is fixed. Nevertheless, there is a linear time algorithm to test ..."
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Cited by 5 (4 self)
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We consider the problem of drawing a graph with a given symmetry such that the number of edge crossings is minimal. We show that this problem is NPhard, even if the order of orbits around the rotation center or along the reection axis is fixed. Nevertheless, there is a linear time algorithm to test planarity and to construct a planar embedding if possible. Finally, we devise an O(m log m) algorithm for computing a crossing minimal drawing if interorbit edges may not cross orbits, showing in particular that intraorbit edges do not contribute to the NPhardness of the crossing minimization problem for symmetries.
A linear time algorithm for constructing maximally symmetric straightline drawings of planar graphs
 Proc. of Graph Drawing 2004
, 2005
"... Abstract Symmetry is one of the most important aesthetic criteria in graph drawing because it reveals structure in the graph. To draw graphs symmetrically, we need two steps. The first step is to find appropriate automorphisms. The second step is to draw the graph to display the automorphisms. Our a ..."
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Cited by 5 (4 self)
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Abstract Symmetry is one of the most important aesthetic criteria in graph drawing because it reveals structure in the graph. To draw graphs symmetrically, we need two steps. The first step is to find appropriate automorphisms. The second step is to draw the graph to display the automorphisms. Our aim in this paper is to construct maximally symmetric straightline drawings of triconnected planar graphs in linear time. Previously known algorithms run in quadratic time. We show that an algorithm of Fontet can be used to find an embedding in the plane with the maximum number of symmetries, and present a new algorithm for finding a straight line drawing that achieves that maximum. Both algorithms run in linear time.
A MaxentStress Model for Graph Layout
"... In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an in ..."
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Cited by 3 (2 self)
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In some applications of graph visualization, input edges have associated target lengths. Dealing with these lengths is a challenge, especially for large graphs. Stress models are often employed in this situation. However, the traditional full stress model is not scalable due to its reliance on an initial allpairs shortest path calculation. A number of fast approximation algorithms have been proposed. While they work well for some graphs, the results are less satisfactory on graphs of intrinsically high dimension, because nodes overlap unnecessarily. We propose a solution, called the maxentstress model, which applies the principle of maximum entropy to cope with the extra degrees of freedom. We describe a forceaugmented stress majorization algorithm that solves the maxentstress model. Numerical results show that the algorithm scales well, and provides acceptable layouts for large, nonrigid graphs. This also has potential applications to scalable algorithms for statistical multidimensional scaling (MDS) with variable distances.
On Nearly Symmetric Drawings of Graphs
"... We propose a forcedirected approach for drawing graphs in a nearly symmetric fashion. Our algorithm is built upon recent theoretical results on maximum symmetric subgraphs. Knowing the sequence of edge contractions sufficient for turning an asymmetric graph into a symmetric subgraph, our approach i ..."
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Cited by 3 (0 self)
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We propose a forcedirected approach for drawing graphs in a nearly symmetric fashion. Our algorithm is built upon recent theoretical results on maximum symmetric subgraphs. Knowing the sequence of edge contractions sufficient for turning an asymmetric graph into a symmetric subgraph, our approach in symmetric drawing begins by drawing a graph's maximum symmetric subgraph using a forcedirected method first; then the contracted edges are reinserted back into the drawing. Considering symmetry as the underlying aesthetic criterion, our algorithm provides better drawings than the conventional spring algorithms, as our experimental results indicate.
Software comprehension  integrating program analysis and software visualization
 in 2nd Conf. on Software Engineering Research and Practise in Sweden
, 2002
"... Abstract — We advocate that successful software comprehension methods (and tools) need the synergy of lowlevel code analyses known from the field of compiler construction, highlevel analyses from the field of reengineering and software visualization techniques. We argue that each individual techn ..."
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Cited by 2 (2 self)
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Abstract — We advocate that successful software comprehension methods (and tools) need the synergy of lowlevel code analyses known from the field of compiler construction, highlevel analyses from the field of reengineering and software visualization techniques. We argue that each individual technique would be either not goal directed or too shallow (or both). After a thorough stateoftheart analysis and a problem discussion, we propose an approach to integration. I.
Computing and drawing isomorphic subgraphs
 Journal of Graph Algorithms and Applications
"... The isomorphic subgraph problem is finding two disjoint subgraphs of a graph which coincide on at least k edges. The graph is partitioned into a subgraph, its copy, and a remainder. The problem resembles the NPhard largest common subgraph problem, which searches copies of a graph in a pair of graph ..."
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Cited by 2 (0 self)
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The isomorphic subgraph problem is finding two disjoint subgraphs of a graph which coincide on at least k edges. The graph is partitioned into a subgraph, its copy, and a remainder. The problem resembles the NPhard largest common subgraph problem, which searches copies of a graph in a pair of graphs. In this paper we show that the isomorphic subgraph problem is NPhard, even for restricted instances such as connected outerplanar graphs. Then we present two different heuristics for the computation of maximal connected isomorphic subgraphs. Both heuristics use weighting functions and have been tested on four independent test suites. Finally, we introduce a spring algorithm which preserves isomorphic subgraphs and displays them as copies of each other. The drawing algorithm yields nice drawings and emphasizes the isomorphic subgraphs.