FO model checking of geometric graphs

D 2018

FO model checking of geometric graphs

HLINĚNÝ, Petr, Filip POKRÝVKA and Bodhayan ROY

Basic information

Original name

FO model checking of geometric graphs

Authors

HLINĚNÝ, Petr (203 Czech Republic, guarantor, belonging to the institution), Filip POKRÝVKA (703 Slovakia, belonging to the institution) and Bodhayan ROY (356 India, belonging to the institution)

Edition

LIPIcs 89. Dagstuhl, 12th International Symposium on Parameterized and Exact Computation (IPEC 2017), p. "19:1"-"19:12", 12 pp. 2018

Publisher

Schloss Dagstuhl--Leibniz-Zentrum fuer 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

RIV identification code

RIV/00216224:14330/18:00100734

Organization unit

Faculty of Informatics

ISBN

978-3-95977-051-4

ISSN

DOI

http://dx.doi.org/10.4230/LIPIcs.IPEC.2017.19

Keywords in English

first-order logic; model checking; fixed-parameter tractability; intersection graphs; visibility graphs

Abstract

V originále

Over the past two decades the main focus of research into first-order (FO) model checking algorithms has been on sparse relational structures – culminating in the FPT algorithm by Grohe, Kreutzer and Siebertz for FO model checking of nowhere dense classes of graphs. On contrary to that, except the case of locally bounded clique-width only little is currently known about FO model checking of dense classes of graphs or other structures. We study the FO model checking problem for dense graph classes definable by geometric means (intersection and visibility graphs). We obtain new nontrivial FPT results, e.g., for restricted subclasses of circular-arc, circle, box, disk, and polygon-visibility graphs. These results use the FPT algorithm by Gajarský et al. for FO model checking of posets of bounded width. We also complement the tractability results by related hardness reductions.

Links

GA17-00837S, research and development project

Name: Strukturální vlastnosti, parametrizovaná řešitelnost a těžkost v kombinatorických problémech

Investor: Czech Science Foundation

MUNI/A/0897/2016, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace VI.

Investor: Masaryk University, Category A

MUNI/A/0992/2016, interní kód MU

Name: Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity (Acronym: SKOMU)

Investor: Masaryk University, Category A

Citovat

HLINĚNÝ, Petr, Filip POKRÝVKA and Bodhayan ROY. FO model checking of geometric graphs. Online. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). LIPIcs 89. Dagstuhl: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2018, p. "19:1"-"19:12", 12 pp. ISBN 978-3-95977-051-4. Available from: https://dx.doi.org/10.4230/LIPIcs.IPEC.2017.19.

@inproceedings{1392993,
   author = {Hliněný, Petr and Pokrývka, Filip and Roy, Bodhayan},
   address = {Dagstuhl},
   booktitle = {12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
   doi = {http://dx.doi.org/10.4230/LIPIcs.IPEC.2017.19},
   edition = {LIPIcs 89},
   keywords = {first-order logic; model checking; fixed-parameter tractability; intersection graphs; visibility graphs},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Dagstuhl},
   isbn = {978-3-95977-051-4},
   pages = {"19:1"-"19:12"},
   publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
   title = {FO model checking of geometric graphs},
   year = {2018}
}

TY  - JOUR
ID  - 1392993
AU  - Hliněný, Petr - Pokrývka, Filip - Roy, Bodhayan
PY  - 2018
TI  - FO model checking of geometric graphs
PB  - Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
CY  - Dagstuhl
SN  - 9783959770514
KW  - first-order logic
KW  - model checking
KW  - fixed-parameter tractability
KW  - intersection graphs
KW  - visibility graphs
N2  - Over the past two decades the main focus of research into first-order (FO) model checking algorithms has been on sparse relational structures – culminating in the FPT algorithm by Grohe, Kreutzer and Siebertz for FO model checking of nowhere dense classes of graphs. On contrary to that, except the case of locally bounded clique-width only little is currently known about FO model checking of dense classes of graphs or other structures. We study the FO model checking problem for dense graph classes definable by geometric means (intersection and visibility graphs). We obtain new nontrivial FPT results, e.g., for restricted subclasses of circular-arc, circle, box, disk, and polygon-visibility graphs. These results use the FPT algorithm by Gajarský et al. for FO model checking of posets of bounded width. We also complement the tractability results by related hardness reductions.
ER  -

HLINĚNÝ, Petr, Filip POKRÝVKA and Bodhayan ROY. FO model checking of geometric graphs. Online. In \textit{12th International Symposium on Parameterized and Exact Computation (IPEC 2017)}. LIPIcs 89. Dagstuhl: Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2018, p.~''19:1''-''19:12'', 12 pp. ISBN~978-3-95977-051-4. Available from: https://dx.doi.org/10.4230/LIPIcs.IPEC.2017.19.

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