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Approximating the Crossing Number of Toroidal Graphs

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Algorithms and Computation (ISAAC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4835))

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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.

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Author information

Authors and Affiliations

  1. FEI, Technical University of Ostrava 17. listopadu 15, 708 33 Ostrava, Czech Republic

    Petr Hliněný

  2. Faculty of Informatics, Masaryk University Botanická 68a, 602 00 Brno, Czech Republic

    Petr Hliněný

  3. Instituto de Física, Universidad Autónoma de San Luis Potosí San Luis Potosí, 78000, Mexico

    Gelasio Salazar

Authors
  1. Petr Hliněný
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  2. Gelasio Salazar
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Editor information

Takeshi Tokuyama

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© 2007 Springer-Verlag Berlin Heidelberg

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Hliněný, P., Salazar, G. (2007). Approximating the Crossing Number of Toroidal Graphs. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_15

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  • DOI: https://doi.org/10.1007/978-3-540-77120-3_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-77118-0

  • Online ISBN: 978-3-540-77120-3

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