Parameterizing above guaranteed values: MaxSat and MaxCut
Journal of Algorithms
Parameterized complexity of finding subgraphs with hereditary properties
Theoretical Computer Science
Faster Fixed Parameter Tractable Algorithms for Undirected Feedback Vertex Set
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
On Feedback Problems in Diagraphs
WG '89 Proceedings of the 15th International Workshop on Graph-Theoretic Concepts in Computer Science
An efficient fixed-parameter algorithm for 3-hitting set
Journal of Discrete Algorithms
On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
SIAM Journal on Discrete Mathematics
Compression-based fixed-parameter algorithms for feedback vertex set and edge bipartization
Journal of Computer and System Sciences
Improved fixed parameter tractable algorithms for two “edge” problems: MAXCUT and MAXDAG
Information Processing Letters
Parameterized complexity of the induced subgraph problem in directed graphs
Information Processing Letters
A fixed-parameter algorithm for the directed feedback vertex set problem
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Fixed-parameter tractability results for feedback set problems in tournaments
Journal of Discrete Algorithms
Parameterized algorithms for d-Hitting Set: The weighted case
Theoretical Computer Science
Breaking the 2n-barrier for Irredundance: Two lines of attack
Journal of Discrete Algorithms
Hardness of subgraph and supergraph problems in c-tournaments
Theoretical Computer Science
Kernels for feedback arc set in tournaments
Journal of Computer and System Sciences
Conflict packing yields linear vertex-kernels for k-FAST, k-dense RTI and a related problem
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Largest induced acyclic tournament in random digraphs: a 2-point concentration
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Fixed-parameter tractability results for feedback set problems in tournaments
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
A faster exact algorithm for the directed maximum leaf spanning tree problem
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
A parameterized route to exact puzzles: breaking the 2n-barrier for irredundance (Extended Abstract)
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Parameterized complexity of eulerian deletion problems
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
A polynomial kernel for feedback arc set on bipartite tournaments
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Fixed-parameter complexity of feedback vertex set in bipartite tournaments
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
An exact exponential-time algorithm for the Directed Maximum Leaf Spanning Tree problem
Journal of Discrete Algorithms
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
A quadratic vertex kernel for feedback arc set in bipartite tournaments
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
A Polynomial Kernel for Feedback Arc Set on Bipartite Tournaments
Theory of Computing Systems
Maximum balanced subgraph problem parameterized above lower bound
Theoretical Computer Science
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The parameterized feedback vertex (arc) set problem is to find whether there are k vertices (arcs) in a given graph whose removal makes the graph acyclic. The parameterized complexity of this problem in general directed graphs is a long standing open problem. We investigate the problems on tournaments, a well studied class of directed graphs. We consider both weighted and unweighted versions.We also address the parametric dual problems which are also natural optimization problems. We show that they are fixed parameter tractable not just in tournaments but in oriented directed graphs (where there is at most one directed arc between a pair of vertices). More specifically, the dual problem we show fixed parameter tractable are: Given an oriented directed graph, is there a subset of k vertices (arcs) that forms an acyclic directed subgraph of the graph?Our main results include: • an O((2.4143)knω)1 algorithm for weighted feedback vertex set problem, and an O((2.415)knω) algorithm for weighted feedback arc set problem in tournaments; • an O((e2k/k)kk2 + min{m Ig n, n2}) algorithm for the dual of feedback vertex set problem (maximum vertex induced acyclic graph) in oriented directed graphs, and an O(4kk + m) algorithm for the dual of feedback arc set problem (maximum arcinduced acyclic graph) in general directed graphs.We also show that the dual of feedback vertex set is W[1]--hard in general directed graphs and the feedback arc set problem is fixed parameter tractable in dense directed graphs. Our results are the first non-trivial results for these problems.