Node Multiway Cut and Subset Feedback Vertex Set on Graphs of Bounded Mim-Width

Abstract The two weighted graph problems Node Multiway Cut (NMC) and Subset Feedback Vertex Set (SFVS) both ask for a vertex set of minimum total weight, that NMC disconnects given terminals, SFVS intersects all cycles containing set. We design meta-algorithm allows to solve in time $$2^{O(rw^3)}\cdot n^{4}$$ 2 O ( r w 3 ) · n 4 , $$2^{O(q^2\log (q))}\cdot q log $$n^{O(k^2)}$$ k where rw is the rank-width, q $${\mathbb {Q}}$$ Q -rank-width, k mim-width decomposition. This answers affirmative an open question raised by Jaffke et al. (Algorithmica 82(1):118–145, 2020) concerning algorithm parameterized mim-width. By unified algorithm, this solves polynomial-time on following classes: Interval Permutation Bi-Interval graphs, Circular Arc Convex - Polygon Dilworth Co- Degenerate graphs fixed ; also Leaf Power if leaf root as input, H -Graphs -representation arbitrary powers above classes. Prior our results, only was known be tractable restricted whereas other results are new.