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(LaTeX) Abstract: |
Given an input graph $G$ on \(n\) vertices and an integer $k$,
the parameterized \textsc{$K_4$-minor cover} problem asks whether there is a set $S$
of at most $k$ vertices whose deletion results in a $K_4$-minor
free graph or, equivalently, in a graph of treewidth at most
$2$. The problem can thus also be called \textsc{Treewidth-$2$
Vertex Deletion}. This problem is inspired by two well-studied
parameterized vertex deletion problems, \textsc{Vertex Cover}
and \textsc{Feedback Vertex Set}, which can be expressed as
\textsc{Treewidth-$t$ Vertex Deletion} problems: $t=0$ for {\sc
Vertex Cover} and $t=1$ for {\sc Feedback Vertex Set}. While
a single-exponential FPT algorithm has been known for a long
time for \textsc{Vertex Cover}, such an algorithm for
\textsc{Feedback Vertex Set} was devised comparatively
recently. While it is known to be unlikely that
\textsc{Treewidth-$t$ Vertex Deletion} can be solved in time
$c^{o(k)}\cdot n^{O(1)}$, it was open whether the \textsc{$K_4$-minor cover} could be
solved in single-exponential FPT time, i.e. in $c^k\cdot
n^{O(1)}$ time. This paper answers this question in the
affirmative. |
URL for the Abstract: |
http://link.springer.com/chapter/10.1007%2F978-3-642-31155-0_11 |
Keywords: |
Parameterized Algorithms, Vertex Deletion Problems, Treewidth |
Copyright Message: |
Copyright Springer-Verlag Berlin Heidelberg 2012. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is
concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965,
in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law.
Published in the Proceedings of SWAT 2012, Helsinki, Finland, July 4-6, 2012. Lecture Notes in Computer Science, Volume 7357. The original publication is available at www.springerlink.com: http://www.springerlink.com/content/q72h573085148563/ |
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