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Parameterized Complexity
TLDR
An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability, and introduces readers to new classes of algorithms which may be analysed more precisely than was the case until now. Expand
Fundamentals of Parameterized Complexity
TLDR
This comprehensive and self-contained textbook presents an accessible overview of the state of the art of multivariate algorithmics and complexity, enabling the reader who masters the complexity issues under discussion to use the positive and negative toolkits in their own research. Expand
On problems without polynomial kernels
TLDR
Using the notion of distillation algorithms, a generic lower-bound engine is developed that allows showing that a variety of FPT problems, fulfilling certain criteria, cannot have polynomial kernels unless the polynomially-bounded hierarchy collapses. Expand
Fixed Parameter Tractability and Completeness
TLDR
It is shown that if Dominating Set is fixed-parameter tractable, then so are a variety of parameterized problems, such as Independent Set, and that for this problem, and for the problem of determining whether a graph has k disjoint cycles, it may take c = 1. Expand
Fixed-Parameter Tractability and Completeness II: On Completeness for W[1]
TLDR
This work shows that INDEPENDENT SET is complete for W, and the W Hierarchy of parameterized problems was defined, and complete problems were identified for the classes W [ t ] for t ⩾ 2. Expand
Polynomial-time data reduction for dominating set
TLDR
It is proved that Dominating Set restricted to planar graphs has a so-called problem kernel of linear size, achieved by two simple and easy-to-implement reduction rules. Expand
Fixed-Parameter Tractability and Completeness I: Basic Results
TLDR
This paper establishes the main results of a completeness program which addresses the apparent fixed-parameter intractability of many parameterized problems and gives a compendium of currently known hardness results. Expand
On the parameterized complexity of multiple-interval graph problems
TLDR
A useful technique for showing W[1]-hardness via a reduction from the k-Multicolored Clique problem, a variant of k-Clique, is developed, which should help in simplifying W-hardness results which are notoriously hard to construct and technically tedious. Expand
Fixed-Parameter Tractability and Completeness IV: On Completeness for W[P] and PSPACE Analogues
TLDR
A number of concrete hardness results for W[P], the top level of the hardness hierarchy introduced by Downey and Fellows in a series of earlier papers, are proved. Expand
Kernelization Algorithms for the Vertex Cover Problem: Theory and Experiments
A variety of efficient kernelization strategies for the classic vertex cover problem are developed, implemented and compared experimentally. A new technique, termed crown reduction, is introduced andExpand
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