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

Abstract

Given a clique-width k-expression of a graph G, we provide 2O(k)⋅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 2O(k)⋅n time algorithm for Feedback Vertex Set. The best running times for all the considered problems were 2O(k⋅log⁡(k))⋅nO(1).