FO Model Checking of Geometric Graphs

Authors Petr Hlineny, Filip Pokrývka, Bodhayan Roy

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Petr Hlineny
Filip Pokrývka
Bodhayan Roy

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Petr Hlineny, Filip Pokrývka, and Bodhayan Roy. FO Model Checking of Geometric Graphs. In 12th International Symposium on Parameterized and Exact Computation (IPEC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 89, pp. 19:1-19:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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


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