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» An Algorithm for the Graph Crossing Number Problem
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STOC
2001
ACM
143views Algorithms» more  STOC 2001»
14 years 6 months ago
Computing crossing numbers in quadratic time
We show that for every fixed ? there is a quadratic time algorithm that decides whether a given graph has crossing number at most and, if this is the case, computes a drawing of t...
Martin Grohe
GD
2006
Springer
13 years 10 months ago
Planar Decompositions and the Crossing Number of Graphs with an Excluded Minor
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
David R. Wood, Jan Arne Telle
COCOA
2007
Springer
14 years 14 days ago
A New Exact Algorithm for the Two-Sided Crossing Minimization Problem
The Two-Sided Crossing Minimization (TSCM) problem calls for minimizing the number of edge crossings of a bipartite graph where the two sets of vertices are drawn on two parallel l...
Lanbo Zheng, Christoph Buchheim
MFCS
2004
Springer
13 years 11 months ago
Crossing Number Is Hard for Cubic Graphs
It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP-hard problem. Their reduction, however, used parallel edges and vertices of very h...
Petr Hlinený
ESA
2008
Springer
115views Algorithms» more  ESA 2008»
13 years 8 months ago
A New Approach to Exact Crossing Minimization
The crossing number problem is to find the smallest number of edge crossings necessary when drawing a graph into the plane. Eventhough the problem is NP-hard, we are interested in ...
Markus Chimani, Petra Mutzel, Immanuel M. Bomze