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SODA
2010
ACM

Approximating the Crossing Number of Graphs Embeddable in Any Orientable Surface

14 years 15 hour ago
Approximating the Crossing Number of Graphs Embeddable in Any Orientable Surface
The crossing number of a graph is the least number of pairwise edge crossings in a drawing of the graph in the plane. We provide an O(n log n) time constant factor approximation algorithm for the crossing number of a graph of bounded maximum degree which is "densely enough" embeddable in any fixed orientable surface. Our approach combines some known tools with a powerful new lower bound on the crossing number of an embedded graph. This result extends previous results that gave such approximations in particular cases of projective, toroidal or apex graphs; it is a qualitative improvement over previously published algorithms that constructed low-crossing-number drawings of embeddable graphs without giving any approximation guarantees. No constant factor approximation algorithms for the crossing number problem over comparably rich classes of graphs are known to date.
Petr Hlineny, Markus Chimani
Added 01 Mar 2010
Updated 02 Mar 2010
Type Conference
Year 2010
Where SODA
Authors Petr Hlineny, Markus Chimani
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