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ABSTRACT:
Objective: Aesthetics are important in algorithm design and graph evaluation. This paper presents two user studies that were conducted to investigate the impact of crossing angles on human graph comprehension.
Method and Results: These two studies together demonstrate our newly proposed twostep approach for testing graph aesthetics. The first study is a controlled experiment with purposelygenerated graphs. Twentytwo subjects participated in the study and were asked to determine the length of a path which was crossed by a set of parallel edges at different angles. The result of an analysis of variance showed that larger crossing angles induced better task performance. The second study was a noncontrolled experiment with general real world graphs. Thirtyseven subjects participated in the study and were asked to find the shortest path of two preselected nodes in a set of graph drawings. The results of simple regression tests confirmed the negative effect of small crossing angles. This study also showed that among our four proposed candidates, the minimum crossing angle on the path was the best measure for the aesthetic when path finding is important.
Conclusion: Larger crossing angles make graphs easier to read.
Implications: In situations where crossings cannot be completely removed (for example, graphs are nonplanar, or a drawing convention is applied), or where effort needed to remove all crossings cannot be justified, the crossing angle should be maximized to reduce the negative impact of crossings to the minimum.
Journal of Visual Languages & Computing 08/2014; 25(4). DOI:10.1016/j.jvlc.2014.03.001 · 0.66 Impact Factor

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We introduce a new string matching problem called orderpreserving matching on numeric strings, where a pattern matches a text if the text contains a substring of values whose relative orders coincide with those of the pattern. Orderpreserving matching is applicable to many scenarios such as stock price analysis and musical melody matching in which the order relations should be matched instead of the strings themselves. Solving orderpreserving matching is closely related to the representation of order relations of a numeric string. We define the prefix representation and the nearest neighbor representation of the pattern, both of which lead to efficient algorithms for orderpreserving matching. We present efficient algorithms for single and multiple pattern cases. For the single pattern case, we give an O(nlogm) time algorithm and optimize it further to obtain O(n+mlogm) time. For the multiple pattern case, we give an O(nlogm) time algorithm.
Theoretical Computer Science 03/2014; 525:68–79. DOI:10.1016/j.tcs.2013.10.006 · 0.52 Impact Factor

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A graph is 1planar if it can be embedded in the plane with at most one crossing per edge. A graph is outer1planar if it has an embedding in which every vertex is on the outer face and each edge has at most one crossing. We present a linear time algorithm to test whether a graph is outer1planar. The algorithm can be used to produce an outer1planar embedding in linear time if it exists.
Algorithmica 01/2014; DOI:10.1007/9783319038414_7 · 0.57 Impact Factor

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A 1planar graph is a graph that can be embedded in the plane with at most one crossing per edge. It is known that testing 1planarity of a graph is NPcomplete.
In this paper, we consider maximal 1planar graphs. A graph G is maximal 1planar if addition of any edge destroys 1planarity of G. We first study combinatorial properties of maximal 1planar embeddings. In particular, we show that in a maximal 1planar embedding, the graph induced by the noncrossing edges is spanning and biconnected.
Using the properties, we show that the problem of testing maximal 1planarity of a graph G can be solved in linear time, if a rotation system Φ (i.e., the circular ordering of edges for each vertex) is given. We also prove that there is at most one maximal 1planar embedding ξ of G that is consistent with the given rotation system Φ. Our algorithm also produces such an embedding in linear time, if it exists.
Theoretical Computer Science 11/2013; 513:65–76. DOI:10.1016/j.tcs.2013.09.029 · 0.52 Impact Factor

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Available from: sydney.edu.au
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ABSTRACT:
Many automatic graph drawing algorithms implement only one or two aesthetic criteria since most aesthetics conflict with each other. Empirical research has shown that although those algorithms are based on different aesthetics, drawings produced by them have comparable effectiveness.The comparable effectiveness raises a question about the necessity of choosing one algorithm against another for drawing graphs when human performance is a main concern. In this paper, we argue that effectiveness can be improved when algorithms are designed by making compromises between aesthetics, rather than trying to satisfy one or two of them to the fullest. We therefore introduce a new algorithm: BIGANGLE. This algorithm produces drawings with multiple aesthetics being improved at the same time, compared to a classical spring algorithm. A user study comparing these two algorithms indicates that BIGANGLE induces a significantly better task performance and a lower cognitive load, therefore resulting in better graph drawings in terms of human cognitive efficiency.Our study indicates that aesthetics should not be considered separately. Improving multiple aesthetics at the same time, even to small extents, will have a better chance to make resultant drawings more effective. Although this finding is based on a study of algorithms, it also applies in general graph visualization and evaluation.
Journal of Visual Languages & Computing 08/2013; 24(4):262–272. DOI:10.1016/j.jvlc.2011.12.002 · 0.66 Impact Factor

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There is strong empirical evidence that human perception of a graph drawing is negatively correlated with the number of edge crossings. However, recent experiments show that one can reduce the negative effect by ensuring that the edges that cross do so at large angles. These experiments have motivated a number of mathematical and algorithmic studies of “right angle crossing (RAC)” drawings of graphs, where the edges cross each other perpendicularly. In this paper we give an algorithm for constructing RAC drawings of “outer1plane” graphs, that is, topological graphs in which each vertex appears on the outer face, and each edge crosses at most one other edge. The drawing algorithm preserves the embedding of the input graph. This is one of the few algorithms available to construct RAC drawings.
International Journal of Computational Geometry & Applications 04/2013; 22(06). DOI:10.1142/S021819591250015X · 0.08 Impact Factor

Source
Available from: SeokHee Hong
[Show abstract]
[Hide abstract]
ABSTRACT:
We introduce a new string matching problem called orderpreserving matching
on numeric strings where a pattern matches a text if the text contains a
substring whose relative orders coincide with those of the pattern.
Orderpreserving matching is applicable to many scenarios such as stock price
analysis and musical melody matching in which the order relations should be
matched instead of the strings themselves. Solving orderpreserving matching
has to do with representations of order relations of a numeric string. We
define prefix representation and nearest neighbor representation, which lead to
efficient algorithms for orderpreserving matching. We present efficient
algorithms for single and multiple pattern cases. For the single pattern case,
we give an O(n log m) time algorithm and optimize it further to obtain O(n + m
log m) time. For the multiple pattern case, we give an O(n log m) time
algorithm.

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Readability criteria have been commonly used to measure the quality of graph visualizations. In this paper we argue that readability criteria, while necessary, are not sufficient. We propose a new kind of criterion, generically termed faithfulness, for evaluating graph layout methods. We propose a general model for quantifying faithfulness, and contrast it with the well established readability criteria. We use examples of multidimensional scaling, edge bundling and several other visualization metaphors (including matrixbased and mapbased visualizations) to illustrate faithfulness.
Visualization Symposium (PacificVis), 2013 IEEE Pacific; 01/2013

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Graph streams have been studied extensively, such as for data mining, while fairly limitedly for visualizations. Recently, edge bundling promises to reduce visual clutter in large graph visualizations, though mainly focusing on static graphs. This paper presents a new framework, namely StreamEB, for edge bundling of graph streams, which integrates temporal, neighbourhood, datadriven and spatial compatibility for edges. Amongst these metrics, temporal and neighbourhood compatibility are introduced for the first time. We then present forcedirected and treebased methods for stream edge bundling. The effectiveness of our framework is then demonstrated using US flights data and ThompsonReuters stock data.
Proceedings of the 20th international conference on Graph Drawing; 09/2012

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ABSTRACT:
Dynamic Social network visualization transforms dynamic information in a social network into geometric representations. Most previous work in this field mainly focuses on the evolution of the overall network.
Visual Languages and HumanCentric Computing (VL/HCC), 2012 IEEE Symposium on; 01/2012

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ABSTRACT:
The crossing resolution of a geometric graph is the minimum crossing angle at which any two edges cross each other. In this paper, we present upper and lower bounds to the crossing resolution of the complete geometric graphs.
Discrete Applied Mathematics 01/2012; 160:132139. DOI:10.1016/j.dam.2011.09.016 · 0.68 Impact Factor

Source
Available from: Giuseppe Liotta
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The classical Fáry's theorem from the 1930s states that every planar graph can be drawn as a straightline drawing. In this paper, we extend Fáry's theorem to nonplanar graphs. More specifically, we study the problem of drawing 1planar graphs with straightline edges. A 1planar graph is a sparse nonplanar graph with at most one crossing per edge. We give a characterisation of those 1planar graphs that admit a straightline drawing. The proof of the characterisation consists of a linear time testing algorithm and a drawing algorithm. We also show that there are 1planar graphs for which every straightline drawing has exponential area. To our best knowledge, this is the first result to extend Fáry's theorem to nonplanar graphs.

Source
Available from: Giuseppe Liotta

Source
Available from: Giuseppe Liotta
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A 2layer drawing represents a bipartite graph where each vertex is a point on one of two parallel lines, no two vertices on the same line are adjacent, and the edges are straightline segments. In this paper we study 2layer drawings where any two crossing edges meet at right angle. We characterize the graphs that admit this type of drawing, provide lineartime testing and embedding algorithms, and present a polynomialtime crossing minimization technique. Also, for a given graph G and a constant k, we prove that it is
$\mathcal{NP}$
complete to decide whether G contains a subgraph of at least k edges having a 2layer drawing with right angle crossings.
Combinatorial Algorithms  22nd International Workshop, IWOCA 2011, Victoria, BC, Canada, July 2022, 2011, Revised Selected Papers; 01/2011

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Edge bundling methods became popular for visualising large dense networks; however, most of previous work mainly relies on geometry to define compatibility between the edges. In this paper, we present a new framework for edge bundling, which tightly integrates topology, geometry and importance. In particular, we introduce new edge compatibility measures, namely importance compatibility and topology compatibility. More specifically, we present four variations of force directed edge bundling method based on the framework: Centralitybased bundling, Radial bundling, Topologybased bundling, and Orthogonal bundling. Our experimental results with social networks, biological networks, geographic networks and clustered graphs indicate that our new framework can be very useful to highlight the most important topological skeletal structures of the input networks.
Graph Drawing  19th International Symposium, GD 2011, Eindhoven, The Netherlands, September 2123, 2011, Revised Selected Papers; 01/2011

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Kozo Sugiyama was born in Gifu Prefecture Japan on September 17, 1945. He received his B.S., M.S., and Dr. Sci. at Nagoya University in 1969, 1971, 1974 respectively. For 23 years from 1974 he was a researcher at Fujitsu. During this time he spent a year at the International Institute for Applied Systems Analysis in Laxenburg in Austria. In the mid 1990s he served as the Director of the Information Processing Society of Japan. In 1997 he moved from Fujitsu to the newlycreated Japan Advanced Institute of Science and Technology. His first position there was Professor of the School of Knowledge Science, but he soon became Director of the Center for Knowledge Science, and then Dean of the School of Knowledge Science. His last few years at JAIST were spent as a Vice President of the University.
Graph Drawing  19th International Symposium, GD 2011, Eindhoven, The Netherlands, September 2123, 2011, Revised Selected Papers; 01/2011

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Available from: ethz.ch
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A Right Angle Crossing Graph (also called a RAC graph for short) is a graph that has a straightline drawing where any two crossing edges are orthogonal to each other. A 11planar graph is a graph that has a drawing where every edge is crossed at most once. This paper studies the combinatorial relationship between the family of RAC graphs and the family of 11planar graphs. It is proved that: (1) all RAC graphs having maximal edge density belong to the intersection of the two families; and (2) there is no inclusion relationship between the two families. As a byproduct of the proof technique, it is also shown that every RAC graph with maximal edge density is the union of two maximal planar graphs.
Graph Drawing  19th International Symposium, GD 2011, Eindhoven, The Netherlands, September 2123, 2011, Revised Selected Papers; 01/2011

Source
Available from: SeokHee Hong
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ABSTRACT:
Recent empirical research has indicated that human graph reading performance improves when crossing angles increase. However, crossing angle has not been used as an aesthetic criterion for graph drawing algorithms so far. In this paper, we introduce a forcedirected method that aims to construct graph drawings with large crossing angles. Experiments indicate that our method significantly increases crossing angles. Surprisingly, the experimental results further demonstrate that the resulting drawings produced by our method have fewer edge crossings, a shorter total edge length and more uniform edge lengths, compared to classical spring algorithms.

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ABSTRACT:
A Right Angle Crossing drawing (RAC drawing for short) of a graph is such that edges can only cross at an angle of . In this paper we provide a characterization of the complete bipartite graphs that admit a straightline RAC drawing.
Information Processing Letters 07/2010; 110(16110):687691. DOI:10.1016/j.ipl.2010.05.023 · 0.48 Impact Factor
