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.
Fundamentals of Parameterized Complexity
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.
On problems without polynomial kernels
Fixed Parameter Tractability and Completeness
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.
Fixed-Parameter Tractability and Completeness II: On Completeness for W
Polynomial-time data reduction for dominating set
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.
Fixed-Parameter Tractability and Completeness I: Basic Results
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.
Fixed-Parameter Tractability and Completeness IV: On Completeness for W[P] and PSPACE Analogues
On the parameterized complexity of multiple-interval graph problems