• DOI:10.4230/LIPIcs.ICALP.2020.18
• Corpus ID: 208909705

A Simple Dynamization of Trapezoidal Point Location in Planar Subdivisions

@article{Brankovic2020ASD,
  title={A Simple Dynamization of Trapezoidal Point Location in Planar Subdivisions},
  author={Milutin Brankovic and Nikola Grujic and Andr{\'e} van Renssen and Martin P. Seybold},
  journal={ArXiv},
  year={2020},
  volume={abs/1912.03389}
}

• Milutin Brankovic, N. Grujic, +1 author M. Seybold
• Published 6 December 2019
• Computer Science
• ArXiv

We study how to dynamize the Trapezoidal Search Tree - a well known randomized point location structure for planar subdivisions of kinetic line segments.
Our approach naturally extends incremental leaf-level insertions to recursive methods and allows adaptation for the online setting. Moreover, the dynamization carries over to the Trapezoidal Search DAG, offering a linear sized data structure with logarithmic point location costs as a by-product. On a set $S$ of non-crossing segments, each update performs expected ${\mathcal O}(\log^2|S|)$ operations.
We demonstrate the practicality of our method with an open-source implementation, based on the Computational Geometry Algorithms Library, and experiments on the update performance.