Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
Faster Fixed Parameter Tractable Algorithms for Undirected Feedback Vertex Set
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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 fixed-parameter algorithms for two feedback set problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
The undirected feedback vertex set problem has a poly(k) kernel
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Invitation to data reduction and problem kernelization
ACM SIGACT News
A fixed-parameter algorithm for the directed feedback vertex set problem
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Planar Feedback Vertex Set and Face Cover: Combinatorial Bounds and Subexponential Algorithms
Graph-Theoretic Concepts in Computer Science
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SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
Querying Protein-Protein Interaction Networks
ISBRA '09 Proceedings of the 5th International Symposium on Bioinformatics Research and Applications
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Algorithmics of Large and Complex Networks
Parameterized graph cleaning problems
Discrete Applied Mathematics
On problems without polynomial kernels
Journal of Computer and System Sciences
A 4k2 kernel for feedback vertex set
ACM Transactions on Algorithms (TALG)
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Preprocessing of min ones problems: a dichotomy
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
A quartic kernel for pathwidth-one vertex deletion
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
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Kernel bounds for disjoint cycles and disjoint paths
Theoretical Computer Science
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Survey: Subexponential parameterized algorithms
Computer Science Review
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Subexponential parameterized algorithms
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Quadratic kernelization for convex recoloring of trees
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
An improved kernel for the undirected planar feedback vertex set problem
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
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In this paper, it is shown that the Feedback Vertex Set problem on unweighted, undirected graphs has a kernel of cubic size. I.e., a polynomial time algorithm is described, that, when given a graph G and an integer k, finds a graph H and integer k′ ≤ k, such that H has a feedback vertex set with at most k′ vertices, if and only if G has a feedback vertex set with at most k vertices, and H has at most O(k3) vertices and edges. This improves upon a result by Burrage et al. [8] who gave a kernel for Feedback Vertex Set of size O(k11). One can easily make the algorithm constructive, and transform a minimum size feedback vertex set of H with at most k′ vertices into a minimum size feedback vertex set of G. The kernelization algorithm can be used as a first step of an FPT algorithm for FEEDBACK VERTEX SET, but also as a preprocessing heuristic for the problem.