TY - GEN

T1 - Deterministic algorithms for the independent feedback vertex set problem

AU - Tamura, Yuma

AU - Ito, Takehiro

AU - Zhou, Xiao

N1 - Funding Information:
We are grateful to Saket Saurabh for fruitful discussions with him. This work is partially supported by JSPS KAKENHI Grant Numbers 25106504 and 25330003.
Publisher Copyright:
© Springer International Publishing Switzerland 2015.

PY - 2015

Y1 - 2015

N2 - A feedback vertex set F of an undirected graph G is a vertex subset of G whose removal results in a forest. Such a set F is said to be independent if F forms an independent set of G. In this paper, we study the problem of finding an independent feedback vertex set of a given graph with the minimum number of vertices, from the viewpoint of graph classes. This problem is NP-hard even for planar bipartite graphs of maximum degree four. However, we show that the problem is solvable in linear time for graphs having tree-like structures, more specifically, for bounded treewidth graphs, chordal graphs and cographs. We then give a fixed-parameter algorithm for planar graphs when parameterized by the solution size. Such a fixed-parameter algorithm is already known for general graphs, but our algorithm is exponentially faster than the known one.

AB - A feedback vertex set F of an undirected graph G is a vertex subset of G whose removal results in a forest. Such a set F is said to be independent if F forms an independent set of G. In this paper, we study the problem of finding an independent feedback vertex set of a given graph with the minimum number of vertices, from the viewpoint of graph classes. This problem is NP-hard even for planar bipartite graphs of maximum degree four. However, we show that the problem is solvable in linear time for graphs having tree-like structures, more specifically, for bounded treewidth graphs, chordal graphs and cographs. We then give a fixed-parameter algorithm for planar graphs when parameterized by the solution size. Such a fixed-parameter algorithm is already known for general graphs, but our algorithm is exponentially faster than the known one.

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U2 - 10.1007/978-3-319-19315-1_31

DO - 10.1007/978-3-319-19315-1_31

M3 - Conference contribution

AN - SCOPUS:84937399576

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 351

EP - 363

BT - Combinatorial Algorithms - 25th International Workshop, IWOCA 2014, Revised Selected Papers

A2 - Froncek, Dalibor

A2 - Kratochvíl, Jan

A2 - Miller, Mirka

PB - Springer Verlag

T2 - 25th International Workshop on Combinatorial Algorithms, IWOCA 2014

Y2 - 15 October 2014 through 17 October 2014

ER -