WG '91 Proceedings of the 17th International Workshop
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Solving Connected Dominating Set Faster than 2 n
Algorithmica - Parameterized and Exact Algorithms
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Improved algorithms for feedback vertex set problems
Journal of Computer and System Sciences
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Linear Kernel for Planar Connected Dominating Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Kernelization: New Upper and Lower Bound Techniques
Parameterized and Exact Computation
A 4k2 kernel for feedback vertex set
ACM Transactions on Algorithms (TALG)
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Solving MAX-r-SAT above a tight lower bound
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A probabilistic approach to problems parameterized above or below tight bounds
Journal of Computer and System Sciences
On feedback vertex set new measure and new structures
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
FPT algorithms for connected feedback vertex set
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Finding odd cycle transversals
Operations Research Letters
Parameterized Complexity
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We investigate a generalization of the classical Feedback Vertex Set (FVS) problem from the point of view of parameterized algorithms. Independent Feedback Vertex Set (IFVS) is the "independent" variant of the FVS problem and is defined as follows: given a graph G and an integer k, decide whether there exists F ⊆ V (G), |F| ≤ k, such that G[V (G) \F] is a forest and G[F] is an independent set; the parameter is k. Note that the similarly parameterized versions of the FVS problem -- where there is no restriction on the graph G[F] -- and its connected variant CFVS -- where G[F] is required to be connected -- have been extensively studied in the literature. The FVS problem easily reduces to the IFVS problem in a manner that preserves the solution size, and so any algorithmic result for IFVS directly carries over to FVS. We show that IFVS can be solved in time O(5k nO(1)) time where n is the number of vertices in the input graph G, and obtain a cubic O(k3)) kernel for the problem. Note the contrast with the CFVS problem, which does not admit a polynomial kernel unless CoNP ⊆ NP/Poly.