FO model checking of interval graphs

Authors:
Robert Ganian;Petr Hliněný;Daniel Král';Jan Obdržálek;Jarett Schwartz;Jakub Teska
Affiliations:
Vienna University of Technology, Austria;Masaryk University, Brno, Czech Republic;University of Warwick, Coventry, United Kingdom;Masaryk University, Brno, Czech Republic;UC Berkeley, Berkeley, United States;University of West Bohemia, Pilsen, Czech Republic
Venue:
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part II
Year:
2013

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Abstract

We study the computational complexity of the FO model checking problem on interval graphs, i.e., intersection graphs of intervals on the real line. The main positive result is that this problem can be solved in time O(n logn) for n-vertex interval graphs with representations containing only intervals with lengths from a prescribed finite set. We complement this result by showing that the same is not true if the lengths are restricted to any set that is dense in some open subset, e.g., in the set (1, 1+ε).