Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detecting Weakly Simple Polygons   A closed curve in the plane is weakly simple if it is the limit (in the
Fr\'echet metric) of a sequence of simple closed curves. We describe an
algorithm to determine whether a closed walk of length n in a simple plane
graph is weakly simple in O(n log n) time, improving an earlier O(n^3)-time
algorithm of Cortese et al. [Discrete Math. 2009]. As an immediate corollary,
we obtain the first efficient algorithm to determine whether an arbitrary
n-vertex polygon is weakly simple; our algorithm runs in O(n^2 log n) time. We
also describe algorithms that detect weak simplicity in O(n log n) time for two
interesting classes of polygons. Finally, we discuss subtle errors in several
previously published definitions of weak simplicity.

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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: eess