Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A randomized polynomial kernel for Subset Feedback Vertex Set   The Subset Feedback Vertex Set problem generalizes the classical Feedback
Vertex Set problem and asks, for a given undirected graph $G=(V,E)$, a set $S
\subseteq V$, and an integer $k$, whether there exists a set $X$ of at most $k$
vertices such that no cycle in $G-X$ contains a vertex of $S$. It was
independently shown by Cygan et al. (ICALP '11, SIDMA '13) and Kawarabayashi
and Kobayashi (JCTB '12) that Subset Feedback Vertex Set is fixed-parameter
tractable for parameter $k$. Cygan et al. asked whether the problem also admits
a polynomial kernelization.
  We answer the question of Cygan et al. positively by giving a randomized
polynomial kernelization for the equivalent version where $S$ is a set of
edges. In a first step we show that Edge Subset Feedback Vertex Set has a
randomized polynomial kernel parameterized by $|S|+k$ with $O(|S|^2k)$
vertices. For this we use the matroid-based tools of Kratsch and Wahlstr\"om
(FOCS '12) that for example were used to obtain a polynomial kernel for
$s$-Multiway Cut. Next we present a preprocessing that reduces the given
instance $(G,S,k)$ to an equivalent instance $(G',S',k')$ where the size of
$S'$ is bounded by $O(k^4)$. These two results lead to a polynomial kernel for
Subset Feedback Vertex Set with $O(k^9)$ vertices.

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The categories of this paper are: econ
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The categories of this paper are: alg-geom
4
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: physics
6
The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin