Fast exact algorithms for some connectivity problems parametrized by clique-width

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.

References in corpus (1)

• Faster Algorithms For Vertex Partitioning Problems Parameterized by Clique-width