Rank Based Approach on Graphs with Structured Neighborhood

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

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

In this paper, we combine the rank-based approach with the notion of $d$-neighbor equivalence to obtain efficient algorithms for several connectivity problems such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree, Longest Induced Path, and Feedback Vertex Set. For all these problems, we obtain $2^{O(k)}\cdot n^{O(1)}$, $2^{O(k \log(k))}\cdot n^{O(1)}$, $2^{O(k^2)}\cdot n^{O(1)}$ and $n^{O(k)}$ time algorithms parameterized respectively by clique-width, $\mathbb{Q}$-rank-width, rank-width and maximum induced matching width. Our approach simplifies and unifies the known algorithms for each of theparameters and match asymptotically also the best time complexity for Vertex Cover and Dominating Set.

Domaines: Algorithme et structure de données [cs.DS]

Mamadou Moustapha Kanté, Benjamin Bergougnoux. Rank Based Approach on Graphs with Structured Neighborhood. 2019. ⟨hal-01799573v3⟩