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. © Springer-Verlag Berlin Heidelberg 2007.
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CITATION STYLE
Hliněný, P., & Salazar, G. (2007). Approximating the crossing number of toroidal graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4835 LNCS, pp. 148–159). Springer Verlag. https://doi.org/10.1007/978-3-540-77120-3_15
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