Acyclic Orientation of Drawings
Journal of Graph Algorithms and Applications, Tome 14 (2010) no. 2, pp. 367-384.

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Given a set of pseudosegments in the plane or a topological graph, we ask for an orientation of the pseudosegments or edges which induces an acyclic orientation on the corresponding planar map. Depending on the maximum number of crossings on a pseudosegment or an edge, we provide algorithms and hardness proofs for this problem.
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     author = {Eyal Ackerman and Kevin Buchin and Christian Knauer and G\"unter Rote},
     title = {Acyclic {Orientation} of {Drawings}},
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Eyal Ackerman; Kevin Buchin; Christian Knauer; Günter Rote. Acyclic Orientation of Drawings. Journal of Graph Algorithms and Applications, Tome 14 (2010) no. 2, pp. 367-384. doi : 10.7155/jgaa.00211. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00211/

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