Parameterized problems complete for nondeterministic FPT time and logarithmic space

Let XNLP be the class of parameterized problems such that an instance of size n with parameter k can be solved nondeterministically in time f(k)nO(1) and space f(k)log⁡(n) (for some computable function f). We give a wide variety of XNLP-complete problems, such as List Coloring and Precoloring Extens...

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Bibliographic Details
Published in:	Information and computation Vol. 300; p. 105195
Main Authors:	Bodlaender, Hans L., Groenland, Carla, Nederlof, Jesper, Swennenhuis, Céline
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.10.2024
ISSN:	0890-5401
Online Access:	Get full text
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Summary:	Let XNLP be the class of parameterized problems such that an instance of size n with parameter k can be solved nondeterministically in time f(k)nO(1) and space f(k)log⁡(n) (for some computable function f). We give a wide variety of XNLP-complete problems, such as List Coloring and Precoloring Extension with pathwidth as parameter, Scheduling of Jobs with Precedence Constraints, with both number of machines and partial order width as parameter, Bandwidth and variants of Weighted CNF-Satisfiability. In particular, this implies that all these problems are W[t]-hard for all t.
ISSN:	0890-5401
DOI:	10.1016/j.ic.2024.105195