# 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} }

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…

## One Citation

A Tail Estimate with Exponential Decay for the Randomized Incremental Construction of Search Structures

- MathematicsSODA
- 2022

A main result is an improved tail bound, with exponential decay, for the size of the TSD: there is a constant such that the probability for a TSD to exceed its expected size by more than this factor is at most 1/e.

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