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Erschienen in:
2011 | OriginalPaper | Buchkapitel
Multicut in Trees Viewed through the Eyes of Vertex Cover
verfasst von : Jianer Chen, Jia-Hao Fan, Iyad A. Kanj, Yang Liu, Fenghui Zhang
Erschienen in: Algorithms and Data Structures
Verlag: Springer Berlin Heidelberg
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We take a new look at the
multicut
problem in trees through the eyes of the
vertex cover
problem. This connection, together with other techniques that we develop, allows us to significantly improve the
O
(
k
6
) upper bound on the kernel size for
multicut
, given by Bousquet et al., to
O
(
k
3
). We exploit this connection further to present a parameterized algorithm for
multicut
that runs in time
O
*
(
ρ
k
), where
$\rho = (\sqrt{5} + 1)/2 \approx 1.618$
. This improves the previous (time) upper bound of
O
*
(2
k
), given by Guo and Niedermeier, for the problem.