Approximating the crossing number of toroidal graphs

Authors:
Petr Hliněný;Gelasio Salazar
Affiliations:
FEI, Technical University of Ostrava, Ostrava, Czech Republic and Faculty of Informatics, Masaryk University, Brno, Czech Republic;Instituto de Física, Universidad Autónoma de San Luis Potosí, San Luis Potosí, Mexico
Venue:
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Year:
2007

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Abstract

CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph drawing and VLSI layout. No polynomial time constant approximation algorithm is known for this NP-complete problem. We prove that a natural approach to planar drawing of toroidal graphs (used already by Pach and Tóth in [21]) gives a polynomial time constant approximation algorithm for the crossing number of toroidal graphs with bounded degree. In this proof we present a new "grid" theorem on toroidal graphs.