Rank Based Approach on Graphs with Structured Neighborhood

05/29/2018

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by   Benjamin Bergougnoux, et al.

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In this paper, we combine the rank-based approach and the neighbor-equivalence to obtain efficient algorithms for several connectivity problems such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree and Feedback Vertex Set. For all these algorithms, we obtain 2^O(k).n^O(1), 2^O(k.log(k)). n^O(1), 2^O(k^2).n^O(1) and n^O(k) time algorithms parameterized respectively by clique-width, Q-rank-width, rank-width and maximum induced matching width, which simplify and unify the known algorithms for each of the parameters and match asymptotically also the best time complexity for Dominating Set.