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@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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