Constructing Many Faces in Arrangements of Lines and Segments

@article{Wang2022ConstructingMF,
  title={Constructing Many Faces in Arrangements of Lines and Segments},
  author={Haitao Wang},
  journal={ArXiv},
  year={2022},
  volume={abs/2110.08669}
}
  • Haitao Wang
  • Published 16 October 2021
  • Computer Science
  • ArXiv
We present new algorithms for computing many faces in arrangements of lines and segments. Given a set S of n lines (resp., segments) and a set P of m points in the plane, the problem is to compute the faces of the arrangements of S that contain at least one point of P . For the line case, we give a deterministic algorithm of O(mn log(n/ √ m)+(m+n) log n) time. This improves the previously best deterministic algorithm [Agarwal, 1990] by a factor of log n and improves the previously best… 

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