Sciweavers

APAL
2007

Bounded fixed-parameter tractability and reducibility

13 years 3 months ago
Bounded fixed-parameter tractability and reducibility
We study a refined framwork of parameterized complexity theory where the parameter dependendence of fixed-parameter tractable algorithms is not arbitrary, but restricted by a function in some family F. For every family F of functions, this yields a notion of F-fixed parameter tractability. If F is the class of all polynomially bounded functions, then F-fixed parameter tractability coincides with polynomial time decidability and if F is the class of all computable functions, F-fixed parameter tractability coincides with the standard notion of fixed-parameter tractability. There are interesting choices of F between these two extremes, for example the class of all singly exponential functions. In this article, we study the general theory of F-fixed parameter tractability. We introduce a generic notion of reduction and two classes F-W[P] and F-XP, which may be viewed as analogues of NP and EXPTIME, respectively, in the world of F-fixed parameter tractability.
Rod Downey, Jörg Flum, Martin Grohe, Mark Wey
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2007
Where APAL
Authors Rod Downey, Jörg Flum, Martin Grohe, Mark Weyer
Comments (0)