FO Model Checking of Interval Graphs

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 FO model checking and successor-invariant FO model checking can be solved in time O(n log n) for n-vertex interval grap...

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Bibliographic Details
Published in:Logical methods in computer science 2015-12, Vol.11, Issue 4
Main Authors: Ganian, Robert, Hlineny, Petr, Kral, Daniel, Obdrzalek, Jan, Schwartz, Jarett, Teska, Jakub
Format: Article
Language:English
Subjects:
computer science - discrete mathematics
computer science - logic in computer science
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Summary: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 FO model checking and successor-invariant FO model checking can be solved in time O(n log n) 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 an open subset, e.g., in the set $(1, 1 + \varepsilon)$.
ISSN:1860-5974
1860-5974
DOI:10.2168/LMCS-11(4:11)2015