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 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. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).