FO model checking on geometric graphs

J 2019

FO model checking on geometric graphs

HLINĚNÝ, Petr, Filip POKRÝVKA and Bodhayan ROY

Basic information

Original name

FO model checking on 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

Computational geometry, Amsterdam, ELSEVIER SCIENCE BV, 2019, 0925-7721

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

URL open access preprint

Impact factor

Impact factor: 0.476

RIV identification code

RIV/00216224:14330/19:00107234

Organization unit

Faculty of Informatics

DOI

http://dx.doi.org/10.1016/j.comgeo.2018.10.001

UT WoS

000452943900001

Keywords in English

first-order logic; model checking; fixed-parameter tractability; intersec- tion 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/1018/2018, interní kód MU

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

Investor: Masaryk University, Category A

MUNI/A/1040/2018, interní kód MU

Name: Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity 19 (Acronym: SKOMU)

Investor: Masaryk University, Category A

Citovat

HLINĚNÝ, Petr, Filip POKRÝVKA and Bodhayan ROY. FO model checking on geometric graphs. Computational geometry. Amsterdam: ELSEVIER SCIENCE BV, 2019, vol. 78, No 1, p. 1-19. ISSN 0925-7721. Available from: https://dx.doi.org/10.1016/j.comgeo.2018.10.001.

@article{1486962,
   author = {Hliněný, Petr and Pokrývka, Filip and Roy, Bodhayan},
   article_location = {Amsterdam},
   article_number = {1},
   doi = {http://dx.doi.org/10.1016/j.comgeo.2018.10.001},
   keywords = {first-order logic; model checking; fixed-parameter tractability; intersec- tion graphs; visibility graphs},
   language = {eng},
   issn = {0925-7721},
   journal = {Computational geometry},
   title = {FO model checking on geometric graphs},
   url = {http://dx.doi.org/10.1016/j.comgeo.2018.10.001},
   volume = {78},
   year = {2019}
}

TY  - JOUR
ID  - 1486962
AU  - Hliněný, Petr - Pokrývka, Filip - Roy, Bodhayan
PY  - 2019
TI  - FO model checking on geometric graphs
JF  - Computational geometry
VL  - 78
IS  - 1
SP  - 1-19
EP  - 1-19
PB  - ELSEVIER SCIENCE BV
SN  - 09257721
KW  - first-order logic
KW  - model checking
KW  - fixed-parameter tractability
KW  - intersec- tion graphs
KW  - visibility graphs
UR  - http://dx.doi.org/10.1016/j.comgeo.2018.10.001
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 on geometric graphs. \textit{Computational geometry}. Amsterdam: ELSEVIER SCIENCE BV, 2019, vol.~78, No~1, p.~1-19. ISSN~0925-7721. Available from: https://dx.doi.org/10.1016/j.comgeo.2018.10.001.

Detailed Information on Publication Record