Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A linear time algorithm to cover and hit a set of line segments
  optimally by two axis-parallel squares   This paper discusses the problem of covering and hitting a set of line
segments $\cal L$ in ${\mathbb R}^2$ by a pair of axis-parallel squares such
that the side length of the larger of the two squares is minimized. We also
discuss the restricted version of covering, where each line segment in $\cal L$
is to be covered completely by at least one square. The proposed algorithm for
the covering problem reports the optimum result by executing only two passes of
reading the input data sequentially. The algorithm proposed for the hitting and
restricted covering problems produces optimum result in $O(n)$ time. All the
proposed algorithms are in-place, and they use only $O(1)$ extra space. The
solution of these problems also give a $\sqrt{2}$ approximation for covering
and hitting those line segments $\cal L$ by two congruent disks of minimum
radius with same computational complexity.

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The categories of this paper are: gr-qc
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The categories of this paper are: math
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The categories of this paper are: cond-mat
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol