Efficient First-Order Model-Checking Using Short Labels

Authors:
Bruno Courcelle;Cyril Gavoille;Mamadou Moustapha Kanté
Affiliations:
LaBRI, CNRS, Université de Bordeaux, France;LaBRI, CNRS, Université de Bordeaux, France;LaBRI, CNRS, Université de Bordeaux, France
Venue:
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Year:
2008

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Abstract

We prove that there exists an O(log(n))-labeling scheme for every first-order formula with free set variables in every class of graphs that is nicely locally cwd-decomposable, which contains in particular, the nicely locally tree-decomposable classes. For every class of graphs of bounded expansionwe prove that every bounded formulahas an O(log(n))-labeling scheme. We also prove that every quantifier-free formula has an O(log(n))-labeling scheme in graphs of bounded arboricity. Some of these results are extended to counting queries.