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arXiv · 1912.03389

A Simple Dynamization of Trapezoidal Point Location in Planar Subdivisions

Milutin Brankovic·Nikola Grujic·André van Renssen·Martin P. Seybold
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Abstract

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.

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Milutin Brankovic, Nikola Grujic, André van Renssen, Martin P. Seybold. 2019-12-06. A Simple Dynamization of Trapezoidal Point Location in Planar Subdivisions. https://arxiv.org/abs/1912.03389

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