Mim-Width II. The Feedback Vertex Set Problemopen access
- Authors
- Kwon, O jung; Jaffke, Lars; Telle, Jan Arne
- Issue Date
- Jan-2020
- Publisher
- SPRINGER
- Citation
- ALGORITHMICA, v.82, no.1, pp.118 - 145
- Indexed
- SCIE
SCOPUS
- Journal Title
- ALGORITHMICA
- Volume
- 82
- Number
- 1
- Start Page
- 118
- End Page
- 145
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/189311
- DOI
- 10.1007/s00453-019-00607-3
- ISSN
- 0178-4617
- Abstract
- We give a first polynomial-time algorithm for (Weighted) Feedback Vertex Set on graphs of bounded maximum induced matching width (mim-width). Explicitly, given a branch decomposition of mim-width w, we give an nO(w)-time algorithm that solves Feedback Vertex Set. This provides a unified polynomial-time algorithm for many well-known classes, such as Interval graphs, Permutation graphs, and Leaf power graphs (given a leaf root), and furthermore, it gives the first polynomial-time algorithms for other classes of bounded mim-width, such as Circular Permutation and Circular k-Trapezoid graphs (given a circular k-trapezoid model) for fixed k. We complement our result by showing that Feedback Vertex Set is W[1]-hard when parameterized by w and the hardness holds even when a linear branch decomposition of mim-width w is given.
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