Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Journal of the ACM (JACM)
On the closest string and substring problems
Journal of the ACM (JACM)
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
Splitters and near-optimal derandomization
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Algorithmic Applications of Low-Distortion Geometric Embeddings
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Distinguishing string selection problems
Information and Computation
On the complexity of finding common approximate substrings
Theoretical Computer Science
On the existence of subexponential parameterized algorithms
Journal of Computer and System Sciences - Special issue on Parameterized computation and complexity
Cuts, Trees and ℓ1-Embeddings of Graphs*
Combinatorica
Low distortion maps between point sets
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Discrete & Computational Geometry
Low-distortion embeddings of general metrics into the line
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The equivalence of theorem proving and the interconnection problem
ACM SIGDA Newsletter
Approximation algorithms for low-distortion embeddings into low-dimensional spaces
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Bidimensionality: new connections between FPT algorithms and PTASs
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Subexponential parameterized algorithms on bounded-genus graphs and H-minor-free graphs
Journal of the ACM (JACM)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)
Approximation algorithms for embedding general metrics into trees
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An O(2O(k)n3) FPT Algorithm for the Undirected Feedback Vertex Set Problem
Theory of Computing Systems
A fixed-parameter algorithm for the directed feedback vertex set problem
Journal of the ACM (JACM)
Efficient Algorithms for the Closest String and Distinguishing String Selection Problems
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Distortion Is Fixed Parameter Tractable
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Randomized algorithms for the loop cutset problem
Journal of Artificial Intelligence Research
Closest Substring Problems with Small Distances
SIAM Journal on Computing
Interval Completion Is Fixed Parameter Tractable
SIAM Journal on Computing
An Exact Algorithm for Minimum Distortion Embedding
Graph-Theoretic Concepts in Computer Science
Bounded fixed-parameter tractability and log2n nondeterministic bits
Journal of Computer and System Sciences
Algorithms for multiterminal cuts
CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
A three-string approach to the closest string problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
More Efficient Algorithms for Closest String and Substring Problems
SIAM Journal on Computing
Random algorithms for the loop cutset problem
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Efficient exact algorithms on planar graphs: exploiting sphere cut branch decompositions
ESA'05 Proceedings of the 13th annual European conference on Algorithms
An O(2O(k)n3) FPT algorithm for the undirected feedback vertex set problem*
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Covering a set of points with a minimum number of lines
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Improved parameterized upper bounds for vertex cover
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Fast algorithms for hard graph problems: bidimensionality, minors, and local treewidth
GD'04 Proceedings of the 12th international conference on Graph Drawing
Improved fixed-parameter algorithms for two feedback set problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Finding odd cycle transversals
Operations Research Letters
Parameterized Complexity
Tight bounds for linkages in planar graphs
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The bounded search tree algorithm for the closest string problem has quadratic smoothed complexity
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Problems parameterized by treewidth tractable in single exponential time: a logical approach
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Faster parameterized algorithms for minor containment
Theoretical Computer Science
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
Graph minors and parameterized algorithm design
The Multivariate Algorithmic Revolution and Beyond
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
On approximating string selection problems with outliers
CPM'12 Proceedings of the 23rd Annual conference on Combinatorial Pattern Matching
On the parameterized complexity of the workflow satisfiability problem
Proceedings of the 2012 ACM conference on Computer and communications security
Enumerating neighbour and closest strings
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Distortion is Fixed Parameter Tractable
ACM Transactions on Computation Theory (TOCT)
On approximating string selection problems with outliers
Theoretical Computer Science
Dynamic programming for graphs on surfaces
ACM Transactions on Algorithms (TALG)
On exact algorithms for the permutation CSP
Theoretical Computer Science
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A central problem in parameterized algorithms is to obtain algorithms with running time f(k) · nO(1) such that f is as slow growing function of the parameter k as possible. In particular, the first natural goal is to make f(k) single-exponential, that is, ck for some constant c. This has led to the development of parameterized algorithms for various problems where f(k) appearing in their running time is of form 2O(k). However there are still plenty of problems where the "slightly superexponential" f(k) appearing in the best known running time has remained non single-exponential even after a lot of attempts to bring it down. A natural question to ask is whether the f(k) appearing in the running time of the best-known algorithms is optimal for any of these problems. In this paper, we examine parameterized problems where f(k) is kO(k) = 2O(k log k) in the best known running time and for a number of such problems, we show that the dependence on k in the running time cannot be improved to single exponential. More precisely we prove following tight lower bounds, for three natural problems, arising from three different domains: • The pattern matching problem Closest String is known to be solvable in time 2O(d log d) · nO(1) and 2O(d log|Σ|) · nO(1). We show that there is no 2o(d log d) · nO(1) and 2o(dlog|Σ|) · nO(1) time algorithm, unless Exponential Time Hypothesis (ETH) fails. • The graph embedding problem Distortion, that is, deciding whether a graph G has a metric embedding into the integers with distortion at most d can be done in time 2O(d log d) · nO(1). We show that there is no 2o(d log d) · nO(1) time algorithm, unless ETH fails. • The Disjoint Paths problem can be solved in time in time 2O(w log w) · nO(1) on graphs of treewidth at most w. We show that there is no 2o(w log w) · nO(1) time algorithm, unless ETH fails. To obtain our result we first prove the lower bound for variants of basic problems: finding cliques, independent sets, and hitting sets. These artificially constrained variants form a good starting point for proving lower bounds on natural problems without any technical restrictions and could be of independent interest. We believe that many further results of this form can be obtained by using the framework of the current paper.