Twin-Width is Linear in the Poset Width

D 2021

Twin-Width is Linear in the Poset Width

BALABÁN, Jakub and Petr HLINĚNÝ

Basic information

Original name

Twin-Width is Linear in the Poset Width

Authors

BALABÁN, Jakub (203 Czech Republic, belonging to the institution) and Petr HLINĚNÝ (203 Czech Republic, guarantor, belonging to the institution)

Edition

214. vyd. Dagstuhl, International Symposium on Parameterized and Exact Computation (IPEC), p. "6:1"-"6:13", 13 pp. 2021

Publisher

Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

URL

RIV identification code

RIV/00216224:14330/21:00119289

Organization unit

Faculty of Informatics

ISBN

978-3-95977-216-7

ISSN

DOI

http://dx.doi.org/10.4230/LIPIcs.IPEC.2021.6

Keywords in English

twin-width; digraph; poset; FO model checking; contraction sequence

Abstract

V originále

Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices, and it extends also to other binary relational structures, e.g. to digraphs and posets. It was introduced just very recently, in 2020 by Bonnet, Kim, Thomasse and Watrigant. One of the core results of these authors is that FO model checking on graph classes of bounded twin-width is in FPT. With that result, they also claimed that posets of bounded width have bounded twin-width, thus capturing prior result on FO model checking of posets of bounded width in FPT. However, their translation from poset width to twin-width was indirect and giving only a very loose double-exponential bound. We prove that posets of width d have twin-width at most 9d with a direct and elegant argument, and show that this bound is asymptotically tight. Specially, for posets of width 2 we prove that in the worst case their twin-width is also equal 2. These two theoretical results are complemented with straightforward algorithms to construct the respective contraction sequence for a given poset.

Links

GA20-04567S, research and development project

Name: Struktura efektivně řešitelných případů těžkých algoritmických problémů na grafech

Investor: Czech Science Foundation

MUNI/A/1108/2020, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace X. (Acronym: SV-FI MAV X.)

Investor: Masaryk University

Citovat

BALABÁN, Jakub and Petr HLINĚNÝ. Twin-Width is Linear in the Poset Width. Online. In Golovach, Petr A. and Zehavi, Meirav. International Symposium on Parameterized and Exact Computation (IPEC). 214th ed. Dagstuhl: Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik, 2021, p. "6:1"-"6:13", 13 pp. ISBN 978-3-95977-216-7. Available from: https://dx.doi.org/10.4230/LIPIcs.IPEC.2021.6.

@inproceedings{1799080,
   author = {Balabán, Jakub and Hliněný, Petr},
   address = {Dagstuhl},
   booktitle = {International Symposium on Parameterized and Exact Computation (IPEC)},
   doi = {http://dx.doi.org/10.4230/LIPIcs.IPEC.2021.6},
   edition = {214},
   editor = {Golovach, Petr A. and Zehavi, Meirav},
   keywords = {twin-width; digraph; poset; FO model checking; contraction sequence},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Dagstuhl},
   isbn = {978-3-95977-216-7},
   pages = {"6:1"-"6:13"},
   publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
   title = {Twin-Width is Linear in the Poset Width},
   url = {https://arxiv.org/abs/2106.15337},
   year = {2021}
}

TY  - JOUR
ID  - 1799080
AU  - Balabán, Jakub - Hliněný, Petr
PY  - 2021
TI  - Twin-Width is Linear in the Poset Width
PB  - Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik
CY  - Dagstuhl
SN  - 9783959772167
KW  - twin-width
KW  - digraph
KW  - poset
KW  - FO model checking
KW  - contraction sequence
UR  - https://arxiv.org/abs/2106.15337
N2  - Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices, and it extends also to other binary relational structures, e.g. to digraphs and posets. It was introduced just very recently, in 2020 by Bonnet, Kim, Thomasse and Watrigant. One of the core results of these authors is that FO model checking on graph classes of bounded twin-width is in FPT. With that result, they also claimed that posets of bounded width have bounded twin-width, thus capturing prior result on FO model checking of posets of bounded width in FPT. However, their translation from poset width to twin-width was indirect and giving only a very loose double-exponential bound. We prove that posets of width d have twin-width at most 9d with a direct and elegant argument, and show that this bound is asymptotically tight. Specially, for posets of width 2 we prove that in the worst case their twin-width is also equal 2. These two theoretical results are complemented with straightforward algorithms to construct the respective contraction sequence for a given poset.
ER  -

BALABÁN, Jakub and Petr HLINĚNÝ. Twin-Width is Linear in the Poset Width. Online. In Golovach, Petr A. and Zehavi, Meirav. \textit{International Symposium on Parameterized and Exact Computation (IPEC)}. 214th ed. Dagstuhl: Schloss Dagstuhl -- Leibniz-Zentrum f$\{\backslash$''u$\}$r Informatik, 2021, p.~''6:1''-''6:13'', 13 pp. ISBN~978-3-95977-216-7. Available from: https://dx.doi.org/10.4230/LIPIcs.IPEC.2021.6.

Detailed Information on Publication Record