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The Balanced Satisfactory Partition Problem

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SOFSEM 2021: Theory and Practice of Computer Science (SOFSEM 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12607))

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Abstract

The Satisfactory Partition problem asks whether it is possible to partition the vertex set of a given undirected graph into two parts such that each vertex has at least as many neighbours in its own part as in the other part. The Balanced Satisfactory Partition problem is a variant of the above problem where the two partite sets are required to have the same cardinality. Both problems are known to be NP-complete but its parameterized complexity remains open until now. We enhance our understanding of the problem from the viewpoint of parameterized complexity. The two main results of the paper are the following: (1) The Satisfactory Partition problem and its balanced version are fixed parameter tractable (FPT) when parametrized by neighbourhood diversity, (2) The Balanced Satisfactory Partition problem is W[1]-hard when parametrized by treewidth.

S. Maity—The author’s research was supported in part by the Science and Engineering Research Board (SERB), Govt. of India, under Sanction Order No. MTR/2018/001025.

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Acknowledgement

The first author gratefully acknowledges support from the Ministry of Human Resource Development, Government of India, under Prime Minister’s Research Fellowship Scheme (No. MRF-192002-211).

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Authors and Affiliations

  1. Indian Institute of Science Education and Research, Pune, 411008, India

    Ajinkya Gaikwad, Soumen Maity & Shuvam Kant Tripathi

Authors
  1. Ajinkya Gaikwad
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  2. Soumen Maity
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  3. Shuvam Kant Tripathi
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Corresponding author

Correspondence to Soumen Maity .

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Editors and Affiliations

  1. Charles University, Prague, Czech Republic

    Tomáš Bureš

  2. University of Bergamo, Bergamo, Italy

    Riccardo Dondi

  3. Free University of Bozen-Bolzano, Bolzano, Italy

    Johann Gamper

  4. University of Genoa, Genoa, Italy

    Giovanna Guerrini

  5. University of Wroclaw, Wroclaw, Poland

    Tomasz Jurdziński

  6. Free University of Bozen-Bolzano, Bolzano, Italy

    Claus Pahl

  7. University Paris Dauphine, Paris, France

    Florian Sikora

  8. University of Liverpool, Liverpool, UK

    Prudence W.H. Wong

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Gaikwad, A., Maity, S., Tripathi, S.K. (2021). The Balanced Satisfactory Partition Problem. In: Bureš, T., et al. SOFSEM 2021: Theory and Practice of Computer Science. SOFSEM 2021. Lecture Notes in Computer Science(), vol 12607. Springer, Cham. https://doi.org/10.1007/978-3-030-67731-2_23

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  • DOI: https://doi.org/10.1007/978-3-030-67731-2_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-67730-5

  • Online ISBN: 978-3-030-67731-2

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