Abstract
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, 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.
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, 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.
| Original language | English |
|---|---|
| Title of host publication | 17th International Symposium on Parameterized and Exact Computation (IPEC 2022) |
| Publication date | 2022 |
| DOIs | |
| Publication status | Published - 2022 |
Keywords
- XNLP
- linear width measures
- parameterized complexity
- hardness proofs
- XP space requirement