A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show that it is NP-hard to compute the crossing number of near-planar graphs. The main idea ...
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n ...
David Eppstein, Michael T. Goodrich, Darren Strash
We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, non-weighted common geometric graphs drawn on n points in the plane in genera...
A geometric graph is a simple graph G = (V, E) with an embedding of the set V in the plane such that the points that represent V are in general position. A geometric graph is said...
We consider online routing algorithms for finding paths between the vertices of plane graphs. Although it has been shown in Bose et al. [4] that there exists no competitive routin...