SIAM Journal on Computing
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Journal of the ACM (JACM)
Fixed-Parameter Tractability and Completeness I: Basic Results
SIAM Journal on Computing
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Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
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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)
Invitation to data reduction and problem kernelization
ACM SIGACT News
Crown reductions for the Minimum Weighted Vertex Cover problem
Discrete Applied Mathematics
Parametric Duality and Kernelization: Lower Bounds and Upper Bounds on Kernel Size
SIAM Journal on Computing
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STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
A quadratic kernel for feedback vertex set
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Incompressibility through Colors and IDs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Lower Bounds for Kernelizations and Other Preprocessing Procedures
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
On problems without polynomial kernels
Journal of Computer and System Sciences
Even Faster Algorithm for Set Splitting!
Parameterized and Exact Computation
A Linear Vertex Kernel for Maximum Internal Spanning Tree
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Graph-modeled data clustering: fixed-parameter algorithms for clique generation
CIAC'03 Proceedings of the 5th Italian conference on Algorithms and complexity
A cubic kernel for feedback vertex set
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses
Proceedings of the forty-second ACM symposium on Theory of computing
Betweenness parameterized above tight lower bound
Journal of Computer and System Sciences
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Preprocessing of min ones problems: a dichotomy
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
A probabilistic approach to problems parameterized above or below tight bounds
Journal of Computer and System Sciences
Solving MAX-r-SAT Above a Tight Lower Bound
Algorithmica
Exact (exponential) algorithms for the dominating set problem
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Parameterized Complexity
Kernelization of packing problems
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Compression via matroids: a randomized polynomial kernel for odd cycle transversal
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Kernelization --- preprocessing with a guarantee
The Multivariate Algorithmic Revolution and Beyond
Studies in computational aspects of voting: open problems of downey and fellows
The Multivariate Algorithmic Revolution and Beyond
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Fixed-Parameter algorithms for minimum cost edge-connectivity augmentation
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Towards optimal kernel for edge-disjoint triangle packing
Information Processing Letters
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Preprocessing (data reduction or kernelization) to reduce instance size is one of the most commonly deployed heuristics in the implementation practice to tackle computationally hard problems. However, a systematic theoretical study of them has remained elusive so far. One of the reasons for this is that if an input to an NP-hard problem can be processed in polynomial time to an equivalent one of smaller size in general, then the preprocessing algorithm can be used to actually solve the problem in polynomial time proving P=NP, which is expected to be unlikely. However the situation regarding systematic study changed drastically with the advent of parameterized complexity. Parameterized complexity provides a natural framework to analyse preprocessing algorithms. In a parameterized problem, every instance x comes with a positive integer, or parameter, k. The problem is said to admit a kernel if, in polynomial time, we can reduce the size of the instance x to a function in k, while preserving the answer. The central notion in parameterized complexity is fixed parameter tractability (FPT), which is the notion of solvability in f(k)@?p(|x|) time for any given instance (x,k), where f is an arbitrary function of the parameter k and p is a polynomial in the input size |x|. It is widely believed that a parameterized problem @P is fixed-parameter tractable if and only if there exists a computable function g(k) such that @P admits a kernel of size g(k). However, the kernels obtained by this theoretical result are usually of exponential (or even worse) sizes, while problem-specific data reductions often achieve quadratic- or even linear-size kernels. So a natural question for any concrete FPT problem is whether it admits polynomial time kernelization to a problem kernel that in the worst case is bounded by a polynomial function of the parameter. Despite several attempts, there are fixed-parameter tractable problems that have only exponential sized kernels. An explanation was provided in a paper by Bodlaender et al. (2009) [8], where it was shown that unless coNP@?NP/poly, there are fixed-parameter tractable problems that cannot have a polynomial sized kernel. This triggered further work on showing lower bounds of kernels, and this article surveys recent developments in the area, starting from the framework developed in the paper by Bodlaender et al. (2009) [8].