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  Crossing minimization problems of drawing bipartite graphs in two clusters [1 citations — 0 self]

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by Lanbo Zheng, Le Song, Peter Eades
ACM International Conference Proceeding Series
http://crpit.com/confpapers/CRPITV45Zheng.pdf
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Abstract:

The crossing minimization problem is a classic and very important problem in graph drawing (Pach, Tòth 1997); the results directly affect the effectiveness of the layout, especially for very large scale graphs. But in many cases crossings cannot be avoided. In this paper we present two models for bipartite graph drawing, aiming to reduce crossings that cannot be avoided in the traditional bilayer drawings. We characterize crossing minimization problems in these models, and prove that they are N P-complete. 1

Citations

304 Some simplified NP-complete graph problems – Garey, Johnson, et al. - 1976
239 Methods for Visual Understanding of Hierarchical Systems – Sugiyama, Tagawa, et al. - 1981
166 Crossing Number is NP-Complete – Garey, Johnson - 1983
72 How to draw a directed graph – Eades, Sugiyama - 1990
54 Graph Drawing: Algorithms for the Visualization of Graphs – Battista, Eades, et al. - 1999
52 Edge crossings in drawings of bipartite graphs – Eades, Wormald - 1994
30 Which crossing number is it, anyway – Pach, Tóth
13 Drawing planar partitions II: HHdrawings – Biedl, Kaufmann, et al. - 1998
5 Nice drawings for planar bipartite graphs – Fomeier, Kaufmann - 1997
2 An improved approximation to the one-sided bilayer drawing – Nagamochi - 2003
1 private comunication – Nagamochi - 2004