Approximating the Crossing Number of Toroidal Graphs

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 T´oth in [20]) 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.

• Type: Conference
• Year: 2007
• Where: ISAAC
• Authors: Petr Hlinený, Gelasio Salazar
• Keywords: Constant Approximation Algorithm, ISAAC 2007, Time Constant Approximation, Toroidal Graphs