Abstract
Crossing minimization problem in a bipartite graph is a well-known NP-Complete problem. Drawing the directed/undirected graphs such that they are easy to understand and remember requires some drawing aesthetics and crossing minimization is one of them. In this paper, we investigate an intelligent evolutionary technique i.e. Genetic Algorithm (GA) for bipartite drawing problem (BDP). Two techniques GA1 and GA2 are proposed based on Genetic Algorithm. It is shown that these techniques outperform previously known heuristics e.g., MinSort (M-Sort) and BaryCenter (BC) as well as a genetic algorithm based level permutation problem (LPP), especially when applied to low density graphs. The solution is tested over various parameter values of genetic bipartite drawing problem. Experimental results show the promising capability of the proposed solution over previously known heuristics.
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References
Mäkinen, E., Sieranta, M.: Genetic Algorithms for Drawing Bipartite Graphs. International Journal of Computer Mathematics 53(3&4), 157–166 (1994)
Bienstock, D.: Some provably hard crossing number problems. In: Proc. 8th Annual ACM Symposium on Computational Geometry, pp. 253–260 (1990)
Garey, M.R., Johnson, D.S.: Crossing number is NP-complete. SIAM J. Algebraic Discrete Methods 4, 312–316 (1983)
Tutte, W.T.: Toward a Theory of Crossing Numbers. J. Comb. Theory 8(1), 45–53 (1970)
Barth, W., Mutzel, P., Junger, M.: Simple and Efficient Bilayer Cross Counting. Journal of Graph Algorithms and Applications (JGAA) 8(2), 179–194 (2004)
Whitley D.: A Genetic Algorithm Tutorial, http://www.cs.uga.edu/~potter/CompIntell/ga_tutorial.pdf
Engelbrecht, A.P.: Computational Intelligence: An Introduction. J. Wiley & Sons, Chichester (2007)
Watkins, M.E.: A special crossing number for bipartite graphs: a research problem. Ann. New York Acad. Sci. 175, 405–410 (1970)
Battista, G.D., Eades, P., Tamassia, R., Tollis, I.: Algorithms for drawing graphs: an annotated bibliography. Comp. Geometry: Theory and Applications 4, 235–282 (1994)
Koebe, M., Knöchel, J.: On the block alignment problem. J. Inf. Process. Cybern. EIK 26, 377–387 (1990)
Sugiyama, K., Tagawa, S., Toda, M.: Methods for visual understanding of hierarchical system structures. IEEE Trans. Syst. Man Cybern. SMC-11, 109–125 (1981)
Abdullah, A.: “Data Mining Using the Crossing Minimization Paradigm,” –Ph.D. Thesis, University of Stirling (2007)
Catarci, T.: The Assignment Heuristic for Crossing Reduction. IEEE Transactions on Systems, Man and Cybernetics 21, 515–521 (1995)
Camel, D., Irene, F.: Breaking Cycles for Minimizing Crossings. Journal of Experimental Algorithmics (JEA) 6 (2001)
Stallmann, M., Brglez, F., Ghosh, D.: Heuristics, Experimental Subjects, and Treatment Evaluation in Bigraph Crossing Minimization. J. Exp. Algorithmics 6 (2001)
Zheng, L., Song, L., Eades, P.: Crossing Minimization Problems of Drawing Bipartite Graphs in Two Clusters. In: ACM Asia-Pacific Symposium on Information Visualization, vol. 109, pp. 33–37 (2005)
Ezziane, Z.: Experimental Comparison between Evolutionary Algorithm and Barycenter Heuristic for the Bipartite Drawing Problem. J. Computer Science 3(9), 717–722 (2007)
Laguna, M., Marti, R., Vails, V.: Arc Crossing Minimization in Hierarchical Digraphs with Tabu Search. Computers and Op. Research 24(12), 1175–1186 (1997)
Martí, R.: Arc Crossing Minimization in Graphs with GRASP. IIE Transactions 33, 913–919 (2004)
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Khan, S., Bilal, M., Sharif, M., Khan, F.A. (2011). A Solution to Bipartite Drawing Problem Using Genetic Algorithm. In: Tan, Y., Shi, Y., Chai, Y., Wang, G. (eds) Advances in Swarm Intelligence. ICSI 2011. Lecture Notes in Computer Science, vol 6728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21515-5_63
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DOI: https://doi.org/10.1007/978-3-642-21515-5_63
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