# An optimal algorithm for intersecting line segments in the plane

@article{Chazelle1992AnOA, title={An optimal algorithm for intersecting line segments in the plane}, author={Bernard Chazelle and Herbert Edelsbrunner}, journal={J. ACM}, year={1992}, volume={39}, pages={1-54} }

The main contribution of this work is an <italic>O</italic>(<italic>n</italic> log <italic>n</italic> + <italic>k</italic>)-time algorithm for computing all <italic>k</italic> intersections among <italic>n</italic> line segments in the plane. This time complexity is easily shown to be optimal. Within the same asymptotic cost, our algorithm can also construct the subdivision of the plane defined by the segments and compute which segment (if any) lies right above (or below) each intersection and…

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