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International Conference on Current Trends in Theory and Practice of Computer Science

SOFSEM 2023: SOFSEM 2023: Theory and Practice of Computer Science pp 159–173Cite as

On the Parameterized Complexity of s-club Cluster Deletion Problems

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13878))

Abstract

We study the parameterized complexity of the \(s\)-Club Cluster Edge Deletion problem: Given a graph G and two integers \(s \ge 2\) and \(k \ge 1\), is it possible to remove at most k edges from G such that each connected component of the resulting graph has diameter at most s? This problem is known to be \(\texttt{NP}\)-hard already when \(s = 2\).We prove that it admits a fixed-parameter tractable algorithm when parameterized by s and the treewidth of the input graph. The same result easily transfers to the case in which we can remove at most k vertices, rather than k edges, from G such that each connected component of the resulting graph has diameter at most s, namely to \(s\)-Club Cluster Vertex Deletion.

This work was partially supported by: (i) MIUR, grant 20174LF3T8 “AHeAD: efficient Algorithms for HArnessing networked Data”; (ii) University of Perugia, Fondi di Ricerca di Ateneo, edizione 2021, project “AIDMIX - Artificial Intelligence for Decision making: Methods for Interpretability and eXplainability”.

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Notes

  1. 1.

    Since the matrix is symmetric, when we update a cell \(D({\partial {C}})[a,b]\) we assume that also \(D({\partial {C}})[b,a]\) is updated with the same value.

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Authors and Affiliations

  1. Dipartimento di Ingegneria, Università degli Studi di Perugia, Perugia, Italy

    Fabrizio Montecchiani, Giacomo Ortali, Tommaso Piselli & Alessandra Tappini

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  1. Fabrizio Montecchiani
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  2. Giacomo Ortali
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  3. Tommaso Piselli
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  4. Alessandra Tappini
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Correspondence to Alessandra Tappini .

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  1. University of Liverpool, Liverpool, UK

    Leszek Gąsieniec

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Montecchiani, F., Ortali, G., Piselli, T., Tappini, A. (2023). On the Parameterized Complexity of s-club Cluster Deletion Problems. In: Gąsieniec, L. (eds) SOFSEM 2023: Theory and Practice of Computer Science. SOFSEM 2023. Lecture Notes in Computer Science, vol 13878. Springer, Cham. https://doi.org/10.1007/978-3-031-23101-8_11

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  • DOI: https://doi.org/10.1007/978-3-031-23101-8_11

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