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@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.
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