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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| Published in: | Information and computation Vol. 300; p. 105195 |
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| Abstract | 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. |
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| AbstractList | 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. |
| ArticleNumber | 105195 |
| Author | Nederlof, Jesper Bodlaender, Hans L. Swennenhuis, Céline Groenland, Carla |
| Author_xml | – sequence: 1 givenname: Hans L. orcidid: 0000-0002-9297-3330 surname: Bodlaender fullname: Bodlaender, Hans L. email: h.l.bodlaender@uu.nl organization: Department of Information and Computing Sciences, Utrecht University, the Netherlands – sequence: 2 givenname: Carla orcidid: 0000-0002-9878-8750 surname: Groenland fullname: Groenland, Carla email: c.e.groenland@tudelft.nl organization: Faculty of Electrical Engineering, Mathematics and Computer Science, Technical University Delft, the Netherlands – sequence: 3 givenname: Jesper surname: Nederlof fullname: Nederlof, Jesper email: j.nederlof@uu.nl organization: Department of Information and Computing Sciences, Utrecht University, the Netherlands – sequence: 4 givenname: Céline surname: Swennenhuis fullname: Swennenhuis, Céline email: c.m.f.swennenhuis@tue.nl organization: Department of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, the Netherlands |
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| Cites_doi | 10.1145/3170442 10.1007/BF02280884 10.1016/0304-3975(76)90061-X 10.1016/S0166-218X(96)00085-6 10.1007/s00453-014-9944-y 10.1137/S0895480194275825 10.1016/0166-218X(89)90031-0 10.1007/s10951-017-0519-z 10.1016/j.ic.2010.11.026 10.1109/TC.1982.1675994 10.1016/0196-6774(84)90006-3 10.1137/S0097539792228228 10.1016/S0304-3975(98)00342-9 10.1016/0890-5401(90)90027-F 10.1145/3154856 10.1007/978-1-4471-5559-1 10.1007/978-1-4612-0515-9 10.1137/0601042 10.1137/0406014 10.1016/j.tcs.2008.09.065 10.1016/j.ic.2014.12.008 10.1016/S0022-0000(03)00078-3 10.1137/0607057 10.1016/0167-6377(95)00031-9 10.1137/S0097539793258143 10.1016/0304-3975(94)00097-3 |
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