Parameterized Complexity
- R. Downey, M. Fellows
- Computer ScienceMonographs in Computer Science
- 6 November 1998
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
- R. Downey, M. Fellows
- Computer ScienceTexts in Computer Science
- 17 December 2013
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
- H. Bodlaender, R. Downey, M. Fellows, D. Hermelin
- Computer ScienceJournal of computer and system sciences (Print)
- 1 December 2009
Fixed Parameter Tractability and Completeness
- R. Downey, M. Fellows
- MathematicsCurrents in Research
- 1992
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[1]
- R. Downey, M. Fellows
- MathematicsTheoretical Computer Science
- 17 April 1995
Polynomial-time data reduction for dominating set
- J. Alber, M. Fellows, R. Niedermeier
- Computer Science, MathematicsJACM
- 16 July 2002
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
- R. Downey, M. Fellows
- MathematicsSIAM journal on computing (Print)
- 1 August 1995
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
- Karl R. Abrahamson, R. Downey, M. Fellows
- MathematicsAnnals of Pure and Applied Logic
- 15 June 1995
On the parameterized complexity of multiple-interval graph problems
- M. Fellows, D. Hermelin, Frances A. Rosamond, Stéphane Vialette
- MathematicsTheoretical Computer Science
- 2009
Parameterized Computational Feasibility
- R. Downey, M. Fellows
- Mathematics
- 1995
This paper surveys one such framework for investigating parameterized computational complexity and presents a number of new results for this theory.
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