Exact and Heuristic Algorithms for 2-Layer Straightline Crossing Minimization

Jünger, Michael and Mutzel, Petra (1996) Exact and Heuristic Algorithms for 2-Layer Straightline Crossing Minimization. In: Symposium on Graph Drawing, GD 1995, September 20-22, 1995, Passau, Germany , pp. 337-348 (Official URL: http://dx.doi.org/10.1007/BFb0021817).

This is the latest version of this item.

Full text not available from this repository.

Abstract

We present algorithms for the two layer straightline crossing minimization problem that are able to compute exact optima.Our computational results lead us to the conclusion that there is no need for heuristics if one layer is fixed, even though the problem is NP-hard, and that for the general problem with two variable layers, true optima can be computed for sparse instances in which the smaller layer contains up to 15 nodes. For bigger instances, the iterated barycenter method turns out to be the method of choice among several popular heuristics whose performance we could assess by comparing the results to optimum solution.

Item Type:Conference Paper
Additional Information:10.1007/BFb0021817
Classifications:G Algorithms and Complexity > G.700 Layering
G Algorithms and Complexity > G.420 Crossings
ID Code:162

Available Versions of this Item

Repository Staff Only: item control page

References

CPLEX: Using the CPLEX callable library and the CPLEX mixed integer library. CPLEX Optimization Inc. (1993)

Dresbach, S.: A New Heuristic Layout Algorithm for DAGs. Derigs, Bachem & Drexl (eds.) Operations Research Proceedings 1994, Springer Verlag, Berlin (1994) 121-126

Dresbach, S.: Personal communication. (1995)

Eades, P., and D. Kelly: Heuristics for Reducing Crossings in 2-Layered Networks. Ars Combinatoria 21-A (1986) 89-98

Eades, P., and N. C. Wormland: Edge crossings in Drawings of Bipartite Graphs. Algorithmica 10 (1994) 379-403

Garey, M. R., and D. S. Johnson: Crossing Number is NP-Complete. SIAM J. on Algebraic and Discrete Methods 4 (1983) 312-316

Grötschel, M., M. Jünger, and G. Reinelt: A cutting plane algorithm for the linear ordering problem. Operations Research 32 (1984) 1195-1220

Grötschel, M., M. Jünger, and G. Reinelt: Optimal triangulation of large real world input-output matrices. Statistische Hefte 25 (1984) 261-295

Grötschel, M., M. Jünger, and G. Reinelt: Facets of the linear ordering polytope. Mathematical Programming 33 (1985) 43-60

Knuth, D. E.: The Stanford GraphBase: A Platform for Combinatorial Computing. ACM Press, Addison-Wesley Publishing Company (1993) New York

Sugiyama, K., S. Tagawa, and M. Toda: Methods for Visual Understanding of Hierarchical System Structures. IEEE Trans. Syst. Man, Cybern., SMC-11 (1981) 109-125

Warfield, J. N.: Crossing Theory and Hierarchy Mapping. IEEE Trans. Syst. Man, Cybern., SMC-7 (1977) 505-523