Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Triangluar Separation of Bichromatic Point Sets in Polygonal
  Environment   Let $\mathcal P$ be a simple polygonal environment with $k$ vertices in the
plane. Assume that a set $B$ of $b$ blue points and a set $R$ of $r$ red points
are distributed in $\mathcal P$. We study the problem of computing triangles
that separate the sets $B$ and $R$, and fall in $\mathcal P$. We call these
triangles \emph{inscribed triangular separators}. We propose an
output-sensitive algorithm to solve this problem in $O(r \cdot
(r+c_B+k)+h_\triangle)$ time, where $c_B$ is the size of convex hull of $B$,
and $h_\triangle$ is the number of inscribed triangular separators. We also
study the case where there does not exist any inscribed triangular separators.
This may happen due to the tight distribution of red points around convex hull
of $B$ while no red points are inside this hull. In this case we focus to
compute a triangle that separates most of the blue points from the red points.
We refer to these triangles as \emph{maximum triangular separators}. Assuming
$n=r+b$, we design a constant-factor approximation algorithm to compute such a
separator in $O(n^{4/3} \log^3 n)$ time. "Eligible for best student paper"

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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: mtrl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph