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
On fixed-parameter tractability and approximability of NP optimization problems
Journal of Computer and System Sciences - special issue on complexity theory
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
Solving large FPT problems on coarse-grained parallel machines
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Tight Lower Bounds for Certain Parameterized NP-Hard Problems
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Upper bounds for vertex cover further improved
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Parameterized Complexity
Confronting hardness using a hybrid approach
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On miniaturized problems in parameterized complexity theory
Theoretical Computer Science - Parameterized and exact computation
On product covering in 3-tier supply chain models: natural complete problems for W[3] and W[4]
Theoretical Computer Science - Algorithmic applications in management
On Recovering Syntenic Blocks from Comparative Maps
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Efficient algorithms for clique problems
Information Processing Letters
Approximability and Fixed-Parameter Tractability for the Exemplar Genomic Distance Problems
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
On Parameterized Exponential Time Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
On problems without polynomial kernels
Journal of Computer and System Sciences
A lower bound on approximation algorithms for the closest substring problem
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
There is no EPTAS for two-dimensional knapsack
Information Processing Letters
Geometric clustering: Fixed-parameter tractability and lower bounds with respect to the dimension
ACM Transactions on Algorithms (TALG)
Journal of Combinatorial Optimization
CPM'06 Proceedings of the 17th Annual conference on Combinatorial Pattern Matching
W-hardness under linear FPT-reductions: structural properties and further applications
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Lower bounds and parameterized approach for longest common subsequence
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
On product covering in supply chain models: natural complete problems for W[3] and W[4]
AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
Parameterized maximum path coloring
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 graph clustering approach to weak motif recognition
WABI'07 Proceedings of the 7th international conference on Algorithms in Bioinformatics
Non-breaking similarity of genomes with gene repetitions
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
The exponential time hypothesis and the parameterized clique problem
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
An exponential time 2-approximation algorithm for bandwidth
Theoretical Computer Science
Parameterized maximum path coloring
Theoretical Computer Science
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We develop new techniques for deriving very strong computational lower bounds for a class of well-known NP-hard problems, including weighted satisfiability, dominating set, hitting set, set cover, clique, and independent set. For example, although a trivial enumeration can easily test in time O(nk) 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) no(k) for any function f, even if we restrict the parameter value k 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 Θ(μ(n)) for any reasonable function μ, no algorithm of running time no(k) can test if a graph of n vertices has a clique of size k. Similar strong lower bounds are also derived for other problems in the above class. Our techniques can be extended to derive computational lower bounds on approximation algorithms 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/ε)no(1/ε) for any function f unless an unlikely collapse occurs in parameterized complexity theory.