Robert Ganian ; Petr Hlineny ; Daniel Kral ; Jan Obdrzalek ; Jarett Schwartz et al. - 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 $(1, 1 + \varepsilon)$.

    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
    Submitted 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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