Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kernels for Below-Upper-Bound Parameterizations of the Hitting Set and
  Directed Dominating Set Problems   In the {\sc Hitting Set} problem, we are given a collection $\cal F$ of
subsets of a ground set $V$ and an integer $p$, and asked whether $V$ has a
$p$-element subset that intersects each set in $\cal F$. We consider two
parameterizations of {\sc Hitting Set} below tight upper bounds: $p=m-k$ and
$p=n-k$. In both cases $k$ is the parameter. We prove that the first
parameterization is fixed-parameter tractable, but has no polynomial kernel
unless coNP$\subseteq$NP/poly. The second parameterization is W[1]-complete,
but the introduction of an additional parameter, the degeneracy of the
hypergraph $H=(V,{\cal F})$, makes the problem not only fixed-parameter
tractable, but also one with a linear kernel. Here the degeneracy of
$H=(V,{\cal F})$ is the minimum integer $d$ such that for each $X\subset V$ the
hypergraph with vertex set $V\setminus X$ and edge set containing all edges of
$\cal F$ without vertices in $X$, has a vertex of degree at most $d.$
  In {\sc Nonblocker} ({\sc Directed Nonblocker}), we are given an undirected
graph (a directed graph) $G$ on $n$ vertices and an integer $k$, and asked
whether $G$ has a set $X$ of $n-k$ vertices such that for each vertex $y\not\in
X$ there is an edge (arc) from a vertex in $X$ to $y$. {\sc Nonblocker} can be
viewed as a special case of {\sc Directed Nonblocker} (replace an undirected
graph by a symmetric digraph). Dehne et al. (Proc. SOFSEM 2006) proved that
{\sc Nonblocker} has a linear-order kernel. We obtain a linear-order kernel for
{\sc Directed Nonblocker}.

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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: atom-ph
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn