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Crossing minimization in extended level drawings of graphs

Christian Bachmaier, Hedi Buchner, Michael Forster, Seok-Hee Hong
2010 Discrete Applied Mathematics  
More specifically, we study minimizing the number of edge crossings in extended level drawings of graphs.  ...  Level drawings are well studied in Graph Drawing due to their strong application for the visualization of hierarchy in graphs.  ...  More precisely, we study the new problem of minimizing the number of edge crossings in extended level drawings of graphs.  ... 
doi:10.1016/j.dam.2009.09.002 fatcat:vwjb7hjidfewrl7o3rll5dadnm

Page 2771 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
Wismath, Fully dy- namic 3-dimensional orthogonal graph drawing (49-58); Vance Waddle and Ashok Malhotra, An E log E line crossing algorithm for levelled graphs (59-71); Michael Jiinger and Sebastian Leipert  ...  , Straight-line drawings of protein in- teractions (259-266); Jaroslav NeSetfil, Art of drawing (towards technology of art) (267-275).  ... 

Some Modifications of Sugiyama Approach [chapter]

Danil E. Baburin
2002 Lecture Notes in Computer Science  
We present a graph drawing algorithm that was developed as an extension of the hierarchical layout method of Sugiyama [4] .  ...  The main features of the algorithm are that the edges are orthogonal and that each edge has at most two bends.  ...  Our task was to eliminate all such crossings and to minimize the number of vertical levels being used. We are solving this problem by constructing a supplementary directed graph G'.  ... 
doi:10.1007/3-540-36151-0_36 fatcat:hpvpnzff5bh45oblgu4qu26nsa

Characterization of Unlabeled Radial Level Planar Graphs [chapter]

J. Joseph Fowler
2010 Lecture Notes in Computer Science  
We characterize the set of unlabeled radial level planar (URLP) graphs that are radial level planar in terms of 7 and 15 forbidden subdivisions depending on whether the graph is disconnected or connected  ...  Suppose that an n-vertex graph has a distinct labeling with the integers {1, . . . , n}. Such a graph is radial level planar if it admits a crossings-free drawing under two constraints.  ...  Both classes of graphs admit radial level planar drawings where an edge of each cycle can wrap around so as to avoid a crossing. We extend the ULP characterization to all URLP graphs as follows: 1.  ... 
doi:10.1007/978-3-642-11805-0_10 fatcat:7uw2vpsljbclrcdxxkcc3wa2re

Guest Editor's Foreword

Seok-Hee Hong
2018 International journal of computational geometry and applications  
The method combines two steps of the Sugiyama framework, levelling and crossing minimization, by finding a level planar graph with respect to some spanning tree in linear time.  ...  The scope of the conference includes various aspects of Information Visualisation, Scientific Visualisation and Graph Drawing.  ... 
doi:10.1142/s0218195918020016 fatcat:jjudamlo3zeadpbvpng4sjcod4

Complexity of Finding Non-Planar Rectilinear Drawings of Graphs [chapter]

Ján Maňuch, Murray Patterson, Sheung-Hung Poon, Chris Thachuk
2011 Lecture Notes in Computer Science  
K-Level Planarization and Crossing Minimization p. 238 On Touching Triangle Graphs p. 250 Triangle Contact Representations and Duality p. 262 On Maximum Differential Graph Coloring p. 274  ...  between Two Large Graphs p. 393 Placing Edge Labels by Modifying an Orthogonal Graph Drawing p. 395 Large Crossing Angles in Circular Layouts p. 397 Graph Drawing Contest Graph Drawing Contest  ... 
doi:10.1007/978-3-642-18469-7_28 fatcat:pxln4k6bzbhxrlde4iufrtt74u

Crossing-constrained hierarchical drawings

Irene Finocchi
2006 Journal of Discrete Algorithms  
the well-known hierarchical approach for creating layered drawings of directed graphs so as to minimize the number of edge crossings while maximizing the number of satisfied constraints.  ...  We study the problem of computing hierarchical drawings of layered graphs when some pairs of edges are not allowed to cross.  ...  A standard method, known as the layer-by-layer sweep heuristic [8, 31] , allows one to reduce crossing minimization in hierarchical drawings to crossing minimization in two-layered drawings where the  ... 
doi:10.1016/j.jda.2005.06.001 fatcat:bgnw7xthnfavrli4h6ozbglqv4

Layered Drawings of Graphs with Crossing Constraints [chapter]

Irene Finocchi
2001 Lecture Notes in Computer Science  
of directed graphs with the capability of minimizing the number of edge crossings while maximizing the number of satisfied non-crossing constraints.  ...  We study the problem of producing hierarchical drawings of layered graphs when some pairs of edges are not allowed to cross.  ...  We also remark that our algorithm can be extended to deal with constraints concerning the relative positions of vertices within each layer.  ... 
doi:10.1007/3-540-44679-6_39 fatcat:vd2pmdqgw5aifgdnljjyv74zlm

A Radial Adaptation of the Sugiyama Framework for Visualizing Hierarchical Information

Christian Bachmaier
2007 IEEE Transactions on Visualization and Computer Graphics  
Particularly, we briefly cover extensions of the level assignment step to benefit by the increasing perimeters of the circles, present three heuristics for crossing reduction in radial level drawings,  ...  In radial drawings of hierarchical graphs the vertices are placed on concentric circles rather than on horizontal lines and the edges are drawn as outwards monotone segments of spirals rather than straight  ...  Acknowledgment The author would like to thank Michael Forster for contributing to the parent papers [15] , [34] and Matthias Höllmüller for expunging some bugs and implementing our algorithms in Gravisto  ... 
doi:10.1109/tvcg.2007.1000 pmid:17356223 fatcat:67eha535r5bangj3dmxsv24o3a

Using a Significant Spanning Tree to Draw a Directed Graph

Martin Harrigan, Patrick Healy
2008 Journal of Graph Algorithms and Applications  
It combines two steps of the Sugiyama framework [31] (leveling and crossing minimization) by finding, in linear time, a leveling of the graph that is level planar with respect to some spanning tree and  ...  In this paper, we present a method of drawing directed graphs that emphasizes a significant spanning tree.  ...  This heuristic has previously been used to determine exact x-coordinates when drawing a directed graph [6] and for the 2-level crossing minimization problem [28] .  ... 
doi:10.7155/jgaa.00168 fatcat:ibb2gopunzclrnxuzuvxmg4xk4

Arc crossing minimization in hierarchical digraphs with tabu search

Manuel Laguna, Rafael Martí, Vicente Valls
1997 Computers & Operations Research  
An important problem in the area of graph drawing is to minimize arc crossings in a multi-layer hierarchical digraph.  ...  Then a tabu search implementation is presented that seeks high-quality drawings by means of an intensification phase that finds a local optimum according to an insertion mechanism and two levels of diversification  ...  Although the most important aesthetic criterion in graph drawing is that of minimizing arc crossings, future work could be directed to extend our procedure to handle additional criteria such as minimization  ... 
doi:10.1016/s0305-0548(96)00083-4 fatcat:i3xydmtc2vgi3g6mhxvt7wbuzy

Multicriteria Scalable Graph Drawing via Stochastic Gradient Descent, (SGD)^2 [article]

Reyan Ahmed, Felice De Luca, Sabin Devkota, Stephen Kobourov, Mingwei Li
2021 arXiv   pre-print
With few exceptions, graph drawing algorithms typically optimize one such criterion, usually at the expense of others.  ...  The approach is scalable and can handle large graphs. A variation of the underlying approach can also be used to optimize many desirable properties in planar graphs, while maintaining planarity.  ...  ACKNOWLEDGMENTS This work was supported in part by NSF grants CCF-1740858, CCF-1712119, and DMS-1839274.  ... 
arXiv:2112.01571v1 fatcat:h4juef7utndftdcefz2c75cioa

Chisio: A Compound Graph Editing and Layout Framework [article]

Cihan Kucukkececi, Ugur Dogrusoz, Esat Belviranli, Alptug Dilek
2017 arXiv   pre-print
We introduce a new free, open-source compound graph editing and layout framework named Chisio, based on the Eclipse Graph Editing Framework (GEF) and written in Java.  ...  Chisio comes with a variety of graph layout algorithms, most supporting compound structures and non-uniform node dimensions.  ...  In other words, a circle of appropriate size is created for each cluster and the nodes in that cluster are placed around this circle trying to minimize edge crossings.  ... 
arXiv:1708.07762v1 fatcat:36ybuuquj5hrhc6c7tfsh2zdge

A Global k-Level Crossing Reduction Algorithm [chapter]

Christian Bachmaier, Franz J. Brandenburg, Wolfgang Brunner, Ferdinand Hübner
2010 Lecture Notes in Computer Science  
Directed graphs are commonly drawn by the Sugiyama algorithm, where crossing reduction is a crucial phase. It is done by repeated one-sided 2-level crossing minimizations, which are still N P-hard.  ...  Our approach is based on the sifting technique and improves the level-by-level heuristics in the hierarchic framework by a further reduction of the number of crossings by 5 -10%.  ...  Summary We have presented an algorithm for the global crossing reduction problem of klevel graphs.  ... 
doi:10.1007/978-3-642-11440-3_7 fatcat:5644wfqds5eydbswzvgwdcbkti

The Aesthetics of Graph Visualization [article]

Chris Bennett, Jody Ryall, Leo Spalteholz, Amy Gooch
2007 Computational Aesthetics in Graphics  
We summarize this in a framework that outlines graph drawing heuristics, their perceptual basis, and evaluation status.  ...  The discipline of graph visualization produces pictorial representations of node–link structures. Much effort has been directed toward making such diagrams visually pleasing.  ...  In the field of graph drawing, a good visualization emphasizes readability and promotes understanding [Fis06] . Research in this area has led to aesthetic heuristics for drawing graphs.  ... 
doi:10.2312/compaesth/compaesth07/057-064 fatcat:m2hj565ayfam3i4wyt7us5viye
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