Genetic algorithms for drawing bipartite graphs

This paper introduces genetic algorithms for the level permutation problem (LPP). The problem is to minimize the number of edge crossings in a bipartite graph when the order of vertices in one of the two vertex subsets is fixed. We show that genetic algorithms outperform the previously known heuristics especially when applied to low density graphs. Values for various parameters of genetic LPP algorithms are tested.

[1]  Daniel Bienstock,et al.  Some provably hard crossing number problems , 1990, SCG '90.

[2]  David S. Johnson,et al.  Crossing Number is NP-Complete , 1983 .

[3]  Mitsuhiko Toda,et al.  Methods for Visual Understanding of Hierarchical System Structures , 1981, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  John N. Warfield,et al.  Crossing Theory and Hierarchy Mapping , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  M. Watkins,et al.  A SPECIAL CROSSING NUMBER FOR BIPARTITE GRAPHS: A RESEARCH PROBLEM , 1970 .

[6]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[7]  Erkki Mäkinen,et al.  Experiments on drawing 2-level hierarchical graphs , 1990, Int. J. Comput. Math..

[8]  W. T. Tutte.  Toward a theory of crossing numbers , 1970 .