Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Characterizing parallel hierarchies by reducibilities
Information Processing Letters
A polynomial algorithm for the k-cut problem for fixed k
Mathematics of Operations Research
The minimum feature set problem
Neural Networks
On limited nondeterminism and the complexity of the V-C dimension
Journal of Computer and System Sciences
Vertex cover: further observations and further improvements
Journal of Algorithms
Which problems have strongly exponential complexity?
Journal of Computer and System Sciences
Combinatorial Approaches to Finding Subtle Signals in DNA Sequences
Proceedings of the Eighth International Conference on Intelligent Systems for Molecular Biology
Exact algorithms for NP-hard problems: a survey
Combinatorial optimization - Eureka, you shrink!
The k-feature set problem is W[2]-complete
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
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
Polynomial algorithm for the k-cut problem
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
W-hardness under linear FPT-reductions: structural properties and further applications
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Approximability and Parameterized Complexity of Minmax Values
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
On Parameterized Exponential Time Complexity
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
On the Compressibility of $\mathcal{NP}$ Instances and Cryptographic Applications
SIAM Journal on Computing
Single parameter FPT-algorithms for non-trivial games
IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
Geometric clustering: Fixed-parameter tractability and lower bounds with respect to the dimension
ACM Transactions on Algorithms (TALG)
Hitting and harvesting pumpkins
ESA'11 Proceedings of the 19th European conference on Algorithms
Editing graphs to satisfy degree constraints: A parameterized approach
Journal of Computer and System Sciences
Lower bounds and parameterized approach for longest common subsequence
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
The complexity of geometric problems in high dimension
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
Hardness of discrepancy computation and ε-net verification in high dimension
Journal of Complexity
On the parameterized complexity of d-dimensional point set pattern matching
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
Parameterized two-player nash equilibrium
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
The parameterized complexity of local search for TSP, more refined
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and 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
A parameterized complexity tutorial
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
A basic parameterized complexity primer
The Multivariate Algorithmic Revolution and Beyond
Parameterized complexity and subexponential-time computability
The Multivariate Algorithmic Revolution and Beyond
European Journal of Combinatorics
Incremental list coloring of graphs, parameterized by conservation
Theoretical Computer Science
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Based on the framework of parameterized complexity theory, we derive tight lower bounds on the computational complexity for a number of well-known NP-hard problems. We start by proving a general result, namely that the parameterized weighted satisfiability problem on depth-t circuits cannot be solved in time n^o^(^k^)m^O^(^1^), where n is the circuit input length, m is the circuit size, and k is the parameter, unless the (t-1)-st level W[t-1] of the W-hierarchy collapses to FPT. By refining this technique, we prove that a group of parameterized NP-hard problems, including weighted sat, hitting set, set cover, and feature set, cannot be solved in time n^o^(^k^)m^O^(^1^), where n is the size of the universal set from which the k elements are to be selected and m is the instance size, unless the first level W[1] of the W-hierarchy collapses to FPT. We also prove that another group of parameterized problems which includes weightedq-sat (for any fixed q=2), clique, independent set, and dominating set, cannot be solved in time n^o^(^k^) unless all search problems in the syntactic class SNP, introduced by Papadimitriou and Yannakakis, are solvable in subexponential time. Note that all these parameterized problems have trivial algorithms of running time either n^km^O^(^1^) or O(n^k).