Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
Parameterized learning complexity
COLT '93 Proceedings of the sixth annual conference on Computational learning theory
On limited nondeterminism and the complexity of the V-C dimension
Journal of Computer and System Sciences
Deciding the Vapnik-Ccaron;ervonenkis dimension is Sp3 -complete
Journal of Computer and System Sciences
On the complexity of database queries
Journal of Computer and System Sciences
New results on monotone dualization and generating hypergraph transversals
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Fixed-Parameter Tractability, Definability, and Model-Checking
SIAM Journal on Computing
Query evaluation via tree-decompositions
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Parameterized complexity for the database theorist
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The Complexity of First-Order and Monadic Second-Order Logic Revisited
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
Parameterized Complexity
Parameterized Complexity and Logic
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Improving exhaustive search implies superpolynomial lower bounds
Proceedings of the forty-second ACM symposium on Theory of computing
Slightly superexponential parameterized problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Some new directions and questions in parameterized complexity
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
The parameterized complexity of maximality and minimality problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
New races in parameterized algorithmics
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Subexponential time and fixed-parameter tractability: exploiting the miniaturization mapping
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
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Motivated by recent results showing that there are natural parameterized problems that are fixed-parameter tractable, but can only be solved by fixed-parameter tractable algorithms the running time of which depends nonelementarily on the parameter, we propose a notion of bounded fixed-parameter tractability, where the dependence of the running time on the parameter is restricted to be singly exponential. We develop a basic theory that is centred around the class EPT of tractable problems and an EW-hierarchy of classes of intractable problems, both in the bounded sense. By and large, this theory is similar to the established unbounded parameterized complexity theory, but there are some remarkable differences. Most notably, certain natural model-checking problems that are known to be fixed-parameter tractable in the unbounded sense have a very high complexity in the bounded theory. The problem of computing the VC-dimension of a family of sets, which is known to be complete for the class W[1] in the unbounded theory, is complete for the class EW[3] in the bounded theory. It turns out that our bounded parameterized complexity theory is closely related to the classical complexity theory of problems that can be solved by a nondeterministic polynomial time algorithm that only uses log^2n nondeterministic bits, and in particular to the classes LOGSNP and LOGNP introduced by Papadimitriou and Yannakakis.