Robert Ganian ; Petr Hlineny ; Daniel Kral ; Jan Obdrzalek ; Jarett Schwartz ; Jakub Teska - FO Model Checking of Interval Graphs

lmcs:1612 - Logical Methods in Computer Science, December 14, 2015, Volume 11, Issue 4 - https://doi.org/10.2168/LMCS-11(4:11)2015
FO Model Checking of Interval GraphsArticle

Authors: Robert Ganian ORCID; Petr Hlineny ORCID; Daniel Kral ORCID; Jan Obdrzalek ; Jarett Schwartz ; Jakub Teska

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 $(1, 1 + \varepsilon)$.

Comment: 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

https://doi.org/10.2168/LMCS-11(4:11)2015
Source: arXiv.org:1302.6043
Volume: Volume 11, Issue 4
Published on: December 14, 2015
Imported on: March 3, 2015
Keywords: Computer Science - Discrete Mathematics, Computer Science - Logic in Computer Science
Licence: arXiv.org - Non-exclusive license to distribute
Funding:
    Source : OpenAIRE Graph
  • Exploiting New Types of Structure for Fixed Parameter Tractability (X-TRACT); Code: P 26696
  • The Parameterized Complexity of Reasoning Problems; Funder: European Commission; Code: 239962
  • Classes of combinatorial objects: from structure to algorithms; Funder: European Commission; Code: 259385

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