Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space

Hans L. Bodlaender; Carla Groenland; Jesper Nederlof; Celine M.F. Swennenhuis

doi:10.1109/FOCS52979.2021.00027

Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space

Hans L. Bodlaender, Carla Groenland, Jesper Nederlof, Celine M.F. Swennenhuis

Eindhoven University of Technology

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

Let XNLP be the class of parameterized prob-lems 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 Coloringand Precoloring Extensionwith pathwidth as parameter, Scheduling Of Jobs With Precedence Constraints, with both number of machines and partial order width as parameter, Bandwidthand variants of Weighted Cnf-satisfiability and reconfiguration problems. In particular, this implies that all these problems are W[t]-hard for all t. This also answers a long standing question on the parameterized complexity of the Bandwidth problem.

Original language	English
Title of host publication	Proceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021
Publisher	IEEE
Pages	193-204
Number of pages	12
ISBN (Electronic)	978-1-6654-2055-6
ISBN (Print)	978-1-6654-2056-3
DOIs	https://doi.org/10.1109/FOCS52979.2021.00027
Publication status	Published - 2022
Event	62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021 - Virtual, Online, United States Duration: 7 Feb 2022 → 10 Feb 2022

Conference

Conference	62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021
Country/Territory	United States
City	Virtual, Online
Period	7/02/22 → 10/02/22

Keywords

Bandwidth
Parameterized complexity
Whierarchy
XNLP

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10.1109/FOCS52979.2021.00027

205500a193Final published version, 591 KBLicence: Taverne

Cite this

@inproceedings{dbdb6578acb042e79a26b6e17e01ef2a,

title = "Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space",

abstract = "Let XNLP be the class of parameterized prob-lems 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 Coloringand Precoloring Extensionwith pathwidth as parameter, Scheduling Of Jobs With Precedence Constraints, with both number of machines and partial order width as parameter, Bandwidthand variants of Weighted Cnf-satisfiability and reconfiguration problems. In particular, this implies that all these problems are W[t]-hard for all t. This also answers a long standing question on the parameterized complexity of the Bandwidth problem.",

keywords = "Bandwidth, Parameterized complexity, Whierarchy, XNLP",

author = "Bodlaender, {Hans L.} and Carla Groenland and Jesper Nederlof and Swennenhuis, {Celine M.F.}",

note = "Publisher Copyright: {\textcopyright} 2022 IEEE.; 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021 ; Conference date: 07-02-2022 Through 10-02-2022",

year = "2022",

doi = "10.1109/FOCS52979.2021.00027",

language = "English",

isbn = "978-1-6654-2056-3",

pages = "193--204",

booktitle = "Proceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021",

publisher = "IEEE",

address = "United States",

}

Bodlaender, HL , Groenland, C , Nederlof, J & Swennenhuis, CMF 2022, Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space. in Proceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021. IEEE, pp. 193-204, 62nd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2021, Virtual, Online, United States, 7/02/22. https://doi.org/10.1109/FOCS52979.2021.00027

Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space. / Bodlaender, Hans L.; Groenland, Carla ; Nederlof, Jesper et al.
Proceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021. IEEE, 2022. p. 193-204.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space

AU - Bodlaender, Hans L.

AU - Groenland, Carla

AU - Nederlof, Jesper

AU - Swennenhuis, Celine M.F.

PY - 2022

Y1 - 2022

N2 - Let XNLP be the class of parameterized prob-lems 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 Coloringand Precoloring Extensionwith pathwidth as parameter, Scheduling Of Jobs With Precedence Constraints, with both number of machines and partial order width as parameter, Bandwidthand variants of Weighted Cnf-satisfiability and reconfiguration problems. In particular, this implies that all these problems are W[t]-hard for all t. This also answers a long standing question on the parameterized complexity of the Bandwidth problem.

AB - Let XNLP be the class of parameterized prob-lems 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 Coloringand Precoloring Extensionwith pathwidth as parameter, Scheduling Of Jobs With Precedence Constraints, with both number of machines and partial order width as parameter, Bandwidthand variants of Weighted Cnf-satisfiability and reconfiguration problems. In particular, this implies that all these problems are W[t]-hard for all t. This also answers a long standing question on the parameterized complexity of the Bandwidth problem.

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BT - Proceedings - 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science, FOCS 2021

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ER -

Parameterized Problems Complete for Nondeterministic FPT time and Logarithmic Space

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Keywords

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