XNLP-completeness for Parameterized Problems on Graphs with a Linear Structure [article]

Hans L. Bodlaender and Carla Groenland and Hugo Jacob and Lars Jaffke and Paloma T. Lima
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,
more » ... and linear mim-width. The problems we consider are Independent Set, Dominating Set, Odd Cycle Transversal, (q-)Coloring, Max Cut, Maximum Regular Induced Subgraph, Feedback Vertex Set, Capacitated (Red-Blue) Dominating Set, and Bipartite Bandwidth.
arXiv:2201.13119v2 fatcat:7ifqqzhjbvcqrpr3lepwbgbwaa