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Twin-Treewidth: A Single-Exponential Logic-Based Approach

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Combinatorial Optimization and Applications (COCOA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14462))

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Abstract

An equivalence class in a set is a subset of elements considered equivalent according to some criterion. This concept is applied to different graph parameters, such as neighborhood diversity, twin-cover, twin-width, and modular width. In this work, we introduce a new parameter in graphs called twin-treewidth, which explores the equivalence classes of twins. This parameter generalizes treewidth and neighborhood diversity, two of the most studied parameters in parameterized complexity. We demonstrate the usefulness of this parameter by proposing a simple exponential-time generic procedure to solve problems that can be expressed in a fragment of a variant of Second-Order Monadic Logic.

This research has received funding from Rio de Janeiro Research Support Foundation (FAPERJ) under grant agreements E-26/201.344/2021 and SEI-260003/001674/2021, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), National Council for Scientific and Technological Development (CNPq) under grant agreement 309832/2020-9.

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Authors and Affiliations

  1. Institute of Computing, Fluminense Federal University, Niterói, Brazil

    Maurício Pires, Uéverton S. Souza & Bruno Lopes

Authors
  1. Maurício Pires
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  2. Uéverton S. Souza
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  3. Bruno Lopes
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Corresponding author

Correspondence to Maurício Pires .

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Editors and Affiliations

  1. University of Texas at Dallas, Richardson, TX, USA

    Weili Wu

  2. Beijing Normal University, Zhuhai, China

    Jianxiong Guo

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Pires, M., Souza, U.S., Lopes, B. (2024). Twin-Treewidth: A Single-Exponential Logic-Based Approach. In: Wu, W., Guo, J. (eds) Combinatorial Optimization and Applications. COCOA 2023. Lecture Notes in Computer Science, vol 14462. Springer, Cham. https://doi.org/10.1007/978-3-031-49614-1_3

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  • DOI: https://doi.org/10.1007/978-3-031-49614-1_3

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  • Online ISBN: 978-3-031-49614-1

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