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

Benjamin Bergougnoux (1) , Mamadou Moustapha Kanté (1) , Mamadou Kanté

1 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes

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.

Mots clés: connected σ ρ-domination.; clique-width; single exponential algorithm; feedback vertex set

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]; Mathématique discrète [cs.DM]

Benjamin Bergougnoux, Mamadou Moustapha Kanté, Mamadou Kanté. Fast exact algorithms for some connectivity problems parametrized by clique-width. 2017. ⟨hal-01560555v2⟩