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
Parameterized complexity of finding regular induced subgraphs
Journal of Discrete Algorithms
A Fixed-Parameter Enumeration Algorithm for the Weighted FVS Problem
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
Iterative Compression for Exactly Solving NP-Hard Minimization Problems
Algorithmics of Large and Complex Networks
Fixed-parameter tractability results for feedback set problems in tournaments
Journal of Discrete Algorithms
Iterative compression and exact algorithms
Theoretical Computer Science
A quartic kernel for pathwidth-one vertex deletion
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems
ACM Transactions on Computation Theory (TOCT)
Feedback vertex set in mixed graphs
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Hitting and harvesting pumpkins
ESA'11 Proceedings of the 19th European conference on Algorithms
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Contracting graphs to paths and trees
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
A single-exponential FPT algorithm for the K4- minor cover problem
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
On group feedback vertex set parameterized by the size of the cutset
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
A faster FPT algorithm for Bipartite Contraction
Information Processing Letters
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We describe an algorithm for the Feedback Vertex Set problem on undirected graphs, parameterizedby the size k of the feedback vertex set, that runs in time O(ckn3) where c = 10.567 and n is the number of vertices in the graph. The best previous algorithms were based on the method of bounded search trees, branching on short cycles. The best previous running time of an FPT algorithm for this problem, due to Raman, Saurabh and Subramanian, has a parameter function of the form 2O(k log k /log log k). Whether an exponentially linear in k FPT algorithm for this problem is possible has been previously noted as a significant challenge. Our algorithm is based on the new FPT technique of iterative compression. Our result holds for a more general form of the problem, where a subset of the vertices may be marked as forbidden to belong to the feedback set. We also establish "exponential optimality" for our algorithm by proving that no FPT algorithm with a parameter function of the form O(2o(k)) is possible, unless there is an unlikely collapse of parameterized complexity classes, namely FPT = M[1].