Approximating the crossing number of toroidal graphs Conference Paper

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Overview

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.

authors

• Hliněný P.
• Salazar Anaya Gelasio

publication date

• 2007-01-01

published in

• Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)  Journal

Research

keywords

• Approximation algorithm; Crossing number; Edge-width; Toroidal graph; Toroidal grid Approximation algorithms; Computational complexity; Edge detection; Polynomials; Theorem proving; Crossing number; Planar drawing; Toroidal graph; Toroidal grid; Graph theory

Identity

Digital Object Identifier (DOI)

• 10.1007/978-3-540-77120-3_15

Additional Document Info

start page

• 148

end page

• 159

volume

• 4835 LNCS