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XNLP-completeness for Parameterized Problems on Graphs with a Linear Structure
[article]
2022
arXiv
pre-print
In this paper, we showcase the class XNLP as a natural place for many hard problems parameterized by linear width measures. This strengthens existing W[1]-hardness proofs for these problems, since XNLP-hardness implies W[t]-hardness for all t. It also indicates, via a conjecture by Pilipczuk and Wrochna [ToCT 2018], that any XP algorithm for such problems is likely to require XP space. In particular, we show XNLP-completeness for natural problems parameterized by pathwidth, linear clique-width,
arXiv:2201.13119v2
fatcat:7ifqqzhjbvcqrpr3lepwbgbwaa