Publication details

On Hardness of the Joint Crossing Number



Year of publication 2015
Type Article in Proceedings
Conference International Symposium on Algorithms and Computation (ISAAC 2015), Lecture Notes in Computer Science 9472
MU Faculty or unit

Faculty of Informatics

Field Informatics
Keywords joint crossing number; crossing minimization
Description The Joint Crossing Number problem asks for a simultaneous embedding of two disjoint graphs into one surface such that the number of edge crossings (between the two graphs) is minimized. It was introduced by Negami in 2001 in connection with diagonal flips in triangulations of surfaces, and subsequently investigated in a general form for small-genus surfaces. We prove that all of the commonly considered variants of this problem are NP-hard already in the orientable surface of genus 6, by a reduction from a special variant of the anchored crossing number problem of Cabello and Mohar.
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