Two New Heuristics for Two-Sided Bipartite Graph Drawing

Two new heuristic strategies are studied based on heuristics for the linear arrangement problem and a stochastic hill-climbing method for the two-sided bipartite crossing number problem. These are compared to the standard heuristic for two-sided bipartite drawing based on iteration of the barycentre method. Our experiments show that they can efficiently find good solutions.

[1]  Helen C. Purchase,et al.  Which Aesthetic has the Greatest Effect on Human Understanding? , 1997, GD.

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

[3]  Richard F. Barrett,et al.  Matrix Market: a web resource for test matrix collections , 1996, Quality of Numerical Software.

[4]  Donald E. Knuth,et al.  The Stanford GraphBase - a platform for combinatorial computing , 1993 .

[5]  Bojan Mohar,et al.  Optimal linear labelings and eigenvalues of graphs , 1992, Discret. Appl. Math..

[6]  David Harel,et al.  A Multi-scale Algorithm for the Linear Arrangement Problem , 2002, WG.

[7]  Camil Demetrescu,et al.  Breaking cycles for minimizing crossings , 2001, JEAL.

[8]  Farhad Shahrokhi,et al.  A new lower bound for the bipartite crossing number with applications , 2000, Theor. Comput. Sci..

[9]  Farhad Shahrokhi,et al.  On Bipartite Drawings and the Linear Arrangement Problem , 2001, SIAM J. Comput..

[10]  Oliver Bastert,et al.  Layered Drawings of Digraphs , 1999, Drawing Graphs.

[11]  Michael Jünger,et al.  Journal of Graph Algorithms and Applications 2-layer Straightline Crossing Minimization: Performance of Exact and Heuristic Algorithms , 2022 .

[12]  Paul Molitor,et al.  Using Sifting for k -Layer Straightline Crossing Minimization , 1999, GD.

[13]  Stefan Dresbach A New Heuristic Layout Algorithm for DAGs , 1995 .

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