Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Threshold Rounding for the Standard LP Relaxation of some Geometric
  Stabbing Problems   In the rectangle stabbing problem, we are given a set $\cR$ of axis-aligned
rectangles in $\RR^2$, and the objective is to find a minimum-cardinality set
of horizontal and/or vertical lines such that each rectangle is intersected by
one of these lines. The standard LP relaxation for this problem is known to
have an integrality gap of 2, while a better intergality gap of 1.58.. is known
for the special case when $\cR$ is a set of horizontal segments. In this paper,
we consider two more special cases: when $\cR$ is a set of horizontal and
vertical segments, and when $\cR$ is a set of unit squares. We show that the
integrality gap of the standard LP relaxation in both cases is stricly less
than $2$. Our rounding technique is based on a generalization of the {\it
threshold rounding} idea used by Kovaleva and Spieksma (SIAM J. Disc. Math
2006), which may prove useful for rounding the LP relaxations of other
geometric covering problems.

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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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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: q-bio
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph