An analytical approach to the partial scan problem
Journal of Electronic Testing: Theory and Applications
A 2-Approximation Algorithm for the Undirected Feedback Vertex Set Problem
SIAM Journal on Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Faster Fixed Parameter Tractable Algorithms for Undirected Feedback Vertex Set
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Randomized algorithms for the loop cutset problem
Journal of Artificial Intelligence Research
Parametric duality and kernelization: lower bounds and upper bounds on kernel size
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Improved fixed-parameter algorithms for two feedback set problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
On parameterized approximability
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Finding odd cycle transversals
Operations Research Letters
Parameterized Complexity
Genome-Scale Computational Approaches to Memory-Intensive Applications in Systems Biology
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Faster fixed parameter tractable algorithms for finding feedback vertex sets
ACM Transactions on Algorithms (TALG)
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
A fixed-parameter algorithm for the directed feedback vertex set problem
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Iterative Compression and Exact Algorithms
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Improved algorithms for feedback vertex set problems
Journal of Computer and System Sciences
A 4k2 kernel for feedback vertex set
ACM Transactions on Algorithms (TALG)
A cubic kernel for feedback vertex set
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
A linear kernel for planar feedback vertex set
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Subset feedback vertex set is fixed-parameter tractable
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Fixed-parameter tractability results for feedback set problems in tournaments
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Improved fixed-parameter algorithms for two feedback set problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
On feedback vertex set new measure and new structures
SWAT'10 Proceedings of the 12th Scandinavian conference on Algorithm Theory
EDGE DOMINATING SET: efficient enumeration-based exact algorithms
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Finding a minimum feedback vertex set in time O(1.7548n)
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
The undirected feedback vertex set problem has a poly(k) kernel
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized problems on coincidence graphs
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
FPT algorithms for connected feedback vertex set
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
FPT algorithms for Connected Feedback Vertex Set
Journal of Combinatorial Optimization
FPT suspects and tough customers: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
Improved algorithms for the feedback vertex set problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Feedback vertex set on graphs of low clique-width
European Journal of 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
Linear kernels and single-exponential algorithms via protrusion decompositions
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We describe an algorithm for the Feedback Vertex Set problem on undirected graphs, parameterized by 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( klogk / loglogk). 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 “annotated” form of the problem, where a subset of the vertices may be marked as not 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].