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FO model checking on geometric graphs

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HLINĚNÝ Petr POKRÝVKA Filip ROY Bodhayan

Rok publikování 2019
Druh Článek v odborném periodiku
Časopis / Zdroj Computational geometry
Fakulta / Pracoviště MU

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Citace
www https://arxiv.org/abs/1709.03701
Doi http://dx.doi.org/10.1016/j.comgeo.2018.10.001
Klíčová slova first-order logic; model checking; fixed-parameter tractability; intersec- tion graphs; visibility graphs
Popis 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.
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