2 Search Results for "Eleftheriadis, Ioannis"

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.137

On Classes of Bounded Tree Rank, Their Interpretations, and Efficient Sparsification

Authors: Jakub Gajarský and Rose McCarty

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

Graph classes of bounded tree rank were introduced recently in the context of the model checking problem for first-order logic of graphs. These graph classes are a common generalization of graph classes of bounded degree and bounded treedepth, and they are a special case of graph classes of bounded expansion. We introduce a notion of decomposition for these classes and show that these decompositions can be efficiently computed. Also, a natural extension of our decomposition leads to a new characterization and decomposition for graph classes of bounded expansion (and an efficient algorithm computing this decomposition). We then focus on interpretations of graph classes of bounded tree rank. We give a characterization of graph classes interpretable in graph classes of tree rank 2. Importantly, our characterization leads to an efficient sparsification procedure: For any graph class 𝒞 interpretable in a graph class of tree rank at most 2, there is a polynomial time algorithm that to any G ∈ 𝒞 computes a (sparse) graph H from a fixed graph class of tree rank at most 2 such that G = I(H) for a fixed interpretation I. To the best of our knowledge, this is the first efficient "interpretation reversal" result that generalizes the result of Gajarský et al. [LICS 2016], who showed an analogous result for graph classes interpretable in classes of graphs of bounded degree.

Cite as

Jakub Gajarský and Rose McCarty. On Classes of Bounded Tree Rank, Their Interpretations, and Efficient Sparsification. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 137:1-137:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{gajarsky_et_al:LIPIcs.ICALP.2024.137,
  author =	{Gajarsk\'{y}, Jakub and McCarty, Rose},
  title =	{{On Classes of Bounded Tree Rank, Their Interpretations, and Efficient Sparsification}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{137:1--137:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.137},
  URN =		{urn:nbn:de:0030-drops-202802},
  doi =		{10.4230/LIPIcs.ICALP.2024.137},
  annote =	{Keywords: First-order model checking, structural graph theory, structural sparsity}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2023.119

Monadic NIP in Monotone Classes of Relational Structures

Authors: Samuel Braunfeld, Anuj Dawar, Ioannis Eleftheriadis, and Aris Papadopoulos

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

We prove that for any monotone class of finite relational structures, the first-order theory of the class is NIP in the sense of stability theory if, and only if, the collection of Gaifman graphs of structures in this class is nowhere dense. This generalises results previously known for graphs to relational structures and answers an open question posed by Adler and Adler (2014). The result is established by the application of Ramsey-theoretic techniques and shows that the property of being NIP is highly robust for monotone classes. We also show that the model-checking problem for first-order logic is intractable on any monotone class of structures that is not (monadically) NIP. This is a contribution towards the conjecture that the hereditary classes of structures admitting fixed-parameter tractable model-checking are precisely those that are monadically NIP.

Cite as

Samuel Braunfeld, Anuj Dawar, Ioannis Eleftheriadis, and Aris Papadopoulos. Monadic NIP in Monotone Classes of Relational Structures. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 119:1-119:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{braunfeld_et_al:LIPIcs.ICALP.2023.119,
  author =	{Braunfeld, Samuel and Dawar, Anuj and Eleftheriadis, Ioannis and Papadopoulos, Aris},
  title =	{{Monadic NIP in Monotone Classes of Relational Structures}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{119:1--119:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.119},
  URN =		{urn:nbn:de:0030-drops-181712},
  doi =		{10.4230/LIPIcs.ICALP.2023.119},
  annote =	{Keywords: Model theory, finite model theory, structural graph theory, model-checking}
}

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1 Braunfeld, Samuel
1 Dawar, Anuj
1 Eleftheriadis, Ioannis
1 Gajarský, Jakub
1 McCarty, Rose
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2 Theory of computation → Finite Model Theory
1 Mathematics of computing → Combinatorics
1 Mathematics of computing → Graph theory
1 Theory of computation → Fixed parameter tractability

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2 structural graph theory
1 First-order model checking
1 Model theory
1 finite model theory
1 model-checking
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