An O(20.304n) Algorithm for Solving Maximum Independent Set Problem
IEEE Transactions on Computers
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Characterizing parallel hierarchies by reducibilities
Information Processing Letters
On limited nondeterminism and the complexity of the V-C dimension
Journal of Computer and System Sciences
Finding maximum independent sets in sparse and general graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
On the complexity of database queries
Journal of Computer and System Sciences
Vertex cover: further observations and further improvements
Journal of Algorithms
Complexity and Approximation: Combinatorial Optimization Problems and Their Approximability Properties
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
A PTAS for Distinguishing (Sub)string Selection
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
On Limited versus Polynomial Nondeterminism
On Limited versus Polynomial Nondeterminism
Solving large FPT problems on coarse-grained parallel machines
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Tight lower bounds for certain parameterized NP-hard problems
Information and Computation
Upper bounds for vertex cover further improved
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Parameterized Complexity
Genus characterizes the complexity of certain graph problems: Some tight results
Journal of Computer and System Sciences
An improved lower bound on approximation algorithms for the Closest Substring problem
Information Processing Letters
On the pseudo-achromatic number problem
Theoretical Computer Science
On the Pseudo-achromatic Number Problem
Graph-Theoretic Concepts in Computer Science
On parameterized exponential time complexity
Theoretical Computer Science
On Parameterized Exponential Time Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
The union of minimal hitting sets: Parameterized combinatorial bounds and counting
Journal of Discrete Algorithms
The union of minimal hitting sets: parameterized combinatorial bounds and counting
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
On the complexity of circuit satisfiability
Proceedings of the forty-second ACM symposium on Theory of computing
Algorithmic lower bounds for problems parameterized by clique-width
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the possibility of faster SAT algorithms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Computing vertex-surjective homomorphisms to partially reflexive trees
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Known algorithms on graphs of bounded treewidth are probably optimal
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The complexity of geometric problems in high dimension
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Safe approximation and its relation to kernelization
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Tight complexity bounds for FPT subgraph problems parameterized by clique-width
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Parameterized complexity and subexponential-time computability
The Multivariate Algorithmic Revolution and Beyond
A tight lower bound for planar multiway cut with fixed number of terminals
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Computing vertex-surjective homomorphisms to partially reflexive trees
Theoretical Computer Science
Maximum cliques in graphs with small intersection number and random intersection graphs
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Parameterized average-case complexity of the hypervolume indicator
Proceedings of the 15th annual conference on Genetic and evolutionary computation
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We develop new techniques for deriving strong computational lower bounds for a class of well-known NP-hard problems. This class includes weighted satisfiability, dominating set, hitting set, set cover, clique, and independent set. For example, although a trivial enumeration can easily test in time O(n^k) if a given graph of n vertices has a clique of size k, we prove that unless an unlikely collapse occurs in parameterized complexity theory, the problem is not solvable in time f(k)n^o^(^k^) for any function f, even if we restrict the parameter values to be bounded by an arbitrarily small function of n. Under the same assumption, we prove that even if we restrict the parameter values k to be of the order @Q(@m(n)) for any reasonable function @m, no algorithm of running time n^o^(^k^) can test if a graph of n vertices has a clique of size k. Similar strong lower bounds on the computational complexity are also derived for other NP-hard problems in the above class. Our techniques can be further extended to derive computational lower bounds on polynomial time approximation schemes for NP-hard optimization problems. For example, we prove that the NP-hard distinguishing substring selection problem, for which a polynomial time approximation scheme has been recently developed, has no polynomial time approximation schemes of running time f(1/@e)n^o^(^1^/^@e^) for any function f unless an unlikely collapse occurs in parameterized complexity theory.