A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
WG '91 Proceedings of the 17th International Workshop
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
Enumerate and Expand: Improved Algorithms for Connected Vertex Cover and Tree Cover
Theory of Computing Systems
Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact Algorithms
On Problems without Polynomial Kernels (Extended Abstract)
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Incompressibility through Colors and IDs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Digraphs: Theory, Algorithms and Applications
Digraphs: Theory, Algorithms and Applications
An O(2O(k)n3) FPT algorithm for the undirected feedback vertex set problem*
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Improved algorithms for the feedback vertex set problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Connecting face hitting sets in planar graphs
Information Processing Letters
Kernelization hardness of connectivity problems in d-degenerate graphs
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
On parameterized independent feedback vertex set
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Kernelization hardness of connectivity problems in d-degenerate graphs
Discrete Applied Mathematics
FPT algorithms for domination in biclique-free graphs
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We study the recently introduced Connected Feedback Vertex Set (CFVS) problem from the view-point of parameterized algorithms. CFVS is the connected variant of the classical Feedback Vertex Set problem and is defined as follows: given a graph G=(V,E) and an integer k, decide whether there exists F⊆V, |F|≤k, such that G[V∖F] is a forest and G[F] is connected. We show that Connected Feedback Vertex Set can be solved in time O(2O(k)nO(1)) on general graphs and in time $O(2^{O(\sqrt{k}\log k)}n^{O(1)})$ on graphs excluding a fixed graph H as a minor. Our result on general undirected graphs uses, as a subroutine, a parameterized algorithm for Group Steiner Tree, a well studied variant of Steiner Tree. We find the algorithm for Group Steiner Tree of independent interest and believe that it could be useful for obtaining parameterized algorithms for other connectivity problems.