Computing crossing numbers in quadratic time

Authors:
Martin Grohe
Affiliations:
Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, 851 S. Morgan St. (M/C 249), Chicago, IL
Venue:
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Year:
2001

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Abstract

We show that for every fixed k\ge 0 there is a quadratic time algorithm that decides whether a given graph has crossing number at most k and, if this is the case, computes a drawing of the graph in the plane with at most k crossings.