Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings

@article{Eppstein2010LinearTimeAF,
  title={Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings},
  author={David Eppstein and Michael T. Goodrich and Darren Strash},
  journal={SIAM J. Comput.},
  year={2010},
  volume={39},
  pages={3814-3829}
}
We provide linear-time algorithms for geometric graphs with sublinearly many edge crossings. That is, we provide algorithms running in $O(n)$ time on connected geometric graphs having $n$ vertices and $k$ pairwise crossings, where $k$ is smaller than $n$ by an iterated logarithmic factor. Specific problems that we study include Voronoi diagrams and single-source shortest paths. Our algorithms all run in linear time in the standard comparison-based computational model; hence, we make no… 

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