Bounded fixed-parameter tractability and reducibility

We study a refined framework of parameterized complexity theory where the parameter dependence 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...

Full description

Saved in:

Bibliographic Details
Published in:	Annals of pure and applied logic Vol. 148; no. 1; pp. 1 - 19
Main Authors:	Downey, Rod, Flum, Jörg, Grohe, Martin, Weyer, Mark
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.09.2007
Subjects:	Parameterized complexity theory Reductions Reductions Parameterized complexity theory
ISSN:	0168-0072
Online Access:	Get full text
Tags:	Add Tag No Tags, Be the first to tag this record!

Description
Summary:	We study a refined framework of parameterized complexity theory where the parameter dependence 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.
ISSN:	0168-0072
DOI:	10.1016/j.apal.2007.06.001