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First-Order Interpretations of Bounded Expansion Classes

Authors Jakub Gajarský, Stephan Kreutzer, Jaroslav Nesetril, Patrice Ossona de Mendez, Michal Pilipczuk, Sebastian Siebertz, Szymon Torunczyk

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Subject Classification

ACM Subject Classification
  • Theory of computation → Logic
  • Theory of computation → Finite Model Theory
Keywords
  • Logical interpretations/transductions
  • structurally sparse graphs
  • bounded expansion

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Abstract

The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter tractable over such graph classes. With the aim of generalizing such results to dense graphs, we introduce classes of graphs with structurally bounded expansion, defined as first-order interpretations of classes of bounded expansion. As a first step towards their algorithmic treatment, we provide their characterization analogous to the characterization of classes of bounded expansion via low treedepth decompositions, replacing treedepth by its dense analogue called shrubdepth.

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Jakub Gajarský, Stephan Kreutzer, Jaroslav Nesetril, Patrice Ossona de Mendez, Michal Pilipczuk, Sebastian Siebertz, and Szymon Torunczyk. First-Order Interpretations of Bounded Expansion Classes. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 126:1-126:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018) https://doi.org/10.4230/LIPIcs.ICALP.2018.126

Author Details

Jakub Gajarský
  • Technical University Berlin, Germany
Stephan Kreutzer
  • Technical University Berlin, Germany
Jaroslav Nesetril
  • Charles University, Prague, Czech Republic
Patrice Ossona de Mendez
  • CAMS (CNRS, UMR 8557), Paris, France
Michal Pilipczuk
  • University of Warsaw, Warsaw, Poland
Sebastian Siebertz
  • University of Warsaw, Warsaw, Poland
Szymon Torunczyk
  • University of Warsaw, Warsaw, Poland

Funding

  • Gajarský, Jakub: J. Gajarský and S. Kreutzer are supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (ERC Consolidator Grant DISTRUCT, grant agreement No 648527).
  • Nesetril, Jaroslav: J. Nešetřil and P. Ossona de Mendez are supported by CE-ITI P202/12/G061 of GACR and European Associated Laboratory (LEA STRUCO).
  • Pilipczuk, Michal: \begin{minipage}[t][1.0cm][b]{0.88\textwidth}M. Pilipczuk and S. Siebertz are supported by the National Science Centre of Poland (NCN) via POLONEZ grant agreement UMO-2015/19/P/ST6/03998, which has received funding from the European Union’s Horizon 2020 research and innovation programme (Marie Skłodowska-Curie grant agreement No. 665778).\end{minipage}\hfil\begin{minipage}[t][0.7cm][b]{0.09\textwidth}\includegraphics[width=38px]{flag_bw}\end{minipage}
  • Torunczyk, Szymon: Sz. Toru{ń}czyk is supported by the NCN grant 2016/21/D/ST6/01485.

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