2013/02/28 by Robert Ganian, Petr Hlineny, Daniel Kral +3 · 1 citation
Computer Science · #cs.DM #cs.LO
paper · pdf · doi:10.2168/lmcs-11(4:11)2015
published as Logical Methods in Computer Science, Volume 11, Issue 4 (December 14, 2015) lmcs:1612 · Paper as accepted to the LMCS journal. An extended abstract of an earlier version of this paper has appeared at ICALP'13. Main changes to the previous version are mostly small improvements in presentation
arxiv created 2015/12/11 · arxiv updated 2017/01/11
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 + ε).