Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Simple Dynamization of Trapezoidal Point Location in Planar
  Subdivisions   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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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio