Fast exact algorithms for some connectivity problems parametrized by clique-width
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Given a clique-width expression of a graph G of clique-width k, we provide 2 O(k) × n O(1) time algorithms for connectivity constraints on locally checkable properties such as Connected Dominating Set, Connected Perfect Dominating Set or Node-Weighted Steiner Tree. We also propose an 2 O(k) × n O(1) time algorithm for Feedback Vertex Set. The best running times for all the considered cases were either 2 O(k×log(k)) × n O(1) .
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