research-article

First-Order Interpretations of Bounded Expansion Classes

Authors:

Jakub Gajarský,

Stephan Kreutzer,

Jaroslav NešETřil,

Patrice Ossona De Mendez,

Michał Pilipczuk,

Sebastian Siebertz,

Szymon ToruńczykAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 21, Issue 4

Article No.: 29, Pages 1 - 41

https://doi.org/10.1145/3382093

Published: 05 July 2020 Publication History

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 transductions 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 covers (or colorings), replacing treedepth by its dense analogue called shrubdepth.

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Cited By

Ossona de Mendez PPilipczuk MSiebertz S(2025)Transducing paths in graph classes with unbounded shrubdepthEuropean Journal of Combinatorics10.1016/j.ejc.2022.103660123(103660)Online publication date: Jan-2025
https://doi.org/10.1016/j.ejc.2022.103660
Gajarský JPilipczuk MSokołowski MStamoulis GToruńczyk SSobocinski PLago UEsparza J(2024)Elementary first-order model checking for sparse graphsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662094(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662094
Schirrmacher NSiebertz SStamoulis GThilikos DVigny ASobocinski PLago UEsparza J(2024)Model Checking Disjoint-Paths Logic on Topological-Minor-Free Graph ClassesProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662089(1-12)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662089
Show More Cited By

Index Terms

First-Order Interpretations of Bounded Expansion Classes
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
2. Theory of computation
  1. Design and analysis of algorithms
    1. Graph algorithms analysis
  2. Logic
    1. Finite Model Theory

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 21, Issue 4

October 2020

330 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/3409647

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

Issue’s Table of Contents

Copyright © 2020 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 July 2020

Online AM: 07 May 2020

Accepted: 01 January 2020

Revised: 01 August 2019

Received: 01 October 2018

Published in TOCL Volume 21, Issue 4

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European Union’s Horizon 2020 research and innovation programme ERC Synergy Grant DYNASNET
European Union’s Horizon 2020 research and innovation programme (Marie Skłodowska-Curie
European Union’s Horizon 2020 research and innovation programme ERC Consolidator Grant DISTRUCT
GAČR, European Associated Laboratory (LEA STRUCO)
NCN
European Research Council (ERC)
National Science Centre of Poland (NCN) via POLONEZ

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Cited By

Ossona de Mendez PPilipczuk MSiebertz S(2025)Transducing paths in graph classes with unbounded shrubdepthEuropean Journal of Combinatorics10.1016/j.ejc.2022.103660123(103660)Online publication date: Jan-2025
https://doi.org/10.1016/j.ejc.2022.103660
Gajarský JPilipczuk MSokołowski MStamoulis GToruńczyk SSobocinski PLago UEsparza J(2024)Elementary first-order model checking for sparse graphsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662094(1-14)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662094
Schirrmacher NSiebertz SStamoulis GThilikos DVigny ASobocinski PLago UEsparza J(2024)Model Checking Disjoint-Paths Logic on Topological-Minor-Free Graph ClassesProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662089(1-12)Online publication date: 8-Jul-2024
https://dl.acm.org/doi/10.1145/3661814.3662089
Grobler MJiang YOssona de Mendez PSiebertz SVigny A(2024)Discrepancy and sparsityJournal of Combinatorial Theory, Series B10.1016/j.jctb.2024.06.001169(96-133)Online publication date: Nov-2024
https://doi.org/10.1016/j.jctb.2024.06.001
Nešetřil JOssona de Mendez PSiebertz S(2024)Modulo-counting first-order logic on bounded expansion classesDiscrete Mathematics10.1016/j.disc.2023.113700347:8(113700)Online publication date: Aug-2024
https://doi.org/10.1016/j.disc.2023.113700
Dreier JMählmann NSiebertz SSaha BServedio R(2023)First-Order Model Checking on Structurally Sparse Graph ClassesProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585186(567-580)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585186
Toruńczyk S(2023)Flip-width: Cops and Robber on dense graphs2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00045(663-700)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00045
Carmesin J(2023)Characterising graphs with no subdivision of a wheel of bounded diameterJournal of Combinatorial Theory, Series B10.1016/j.jctb.2023.01.004161(21-51)Online publication date: Jul-2023
https://doi.org/10.1016/j.jctb.2023.01.004
Jiang YNešetřil JOssona de Mendez P(2023)From χ- to χ-bounded classesJournal of Combinatorial Theory, Series B10.1016/j.jctb.2021.05.006158(186-209)Online publication date: Jan-2023
https://doi.org/10.1016/j.jctb.2021.05.006
Bonnet ÉDreier JGajarský JKreutzer SMählmann NSimon PToruńczyk S(2022)Model Checking on Interpretations of Classes of Bounded Local CliquewidthProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533367(1-13)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533367
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