Emergent Mind
Fast exact algorithms for some connectivity problems parametrized by clique-width
(1707.03584)
Published Jul 12, 2017
in
cs.CC
,
cs.DM
,
and
cs.DS
Abstract
Given a clique-width $k$-expression of a graph $G$, we provide $2{O(k)}\cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex Cover. We also propose a $2{O(k)}\cdot n$ time algorithm for Feedback Vertex Set. The best running times for all the considered cases were either $2{O(k\cdot \log(k))}\cdot n{O(1)}$ or worse.
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