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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2022: Graph-Theoretic Concepts in Computer Science pp 201–214Cite as

On the Lossy Kernelization for Connected Treedepth Deletion Set

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13453))

Abstract

We study the Connected \(\eta \) -Treedepth Deletion problem, where the input instance is an undirected graph G, and an integer k and the objective is to decide whether there is a vertex set \(S \subseteq V(G)\) such that \(|S| \le k\), every connected component of \(G - S\) has treedepth at most \(\eta \) and G[S] is a connected graph. As this problem naturally generalizes the well-studied Connected Vertex Cover problem, when parameterized by the solution size k, Connected \(\eta \) -Treedepth Deletion is known to not admit a polynomial kernel unless \(\mathsf{NP \subseteq coNP/poly}\). This motivates the question of designing approximate polynomial kernels for this problem.

In this paper, we show that for every fixed \(0 < \varepsilon \le 1\), Connected \(\eta \) -Treedepth Deletion admits a time-efficient \((1+\varepsilon )\)-approximate kernel of size \(k^{2^{{\mathcal O}(\eta + 1/\varepsilon )}}\) (i.e., a Polynomial-size Approximate Kernelization Scheme).

M. S. Ramanujan is supported by Engineering and Physical Sciences Research Council (EPSRC) grants EP/V007793/1 and EP/V044621/1.

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Notes

  1. 1.

    Due to lack of space, omitted proofs or the proofs marked \(\star \) can be found in the full version.

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Author information

Authors and Affiliations

  1. Royal Holloway, University of London, Egham, UK

    Eduard Eiben

  2. Indraprastha Institute of Information Technology Delhi, New Delhi, India

    Diptapriyo Majumdar

  3. University of Warwick, Coventry, UK

    M. S. Ramanujan

Authors
  1. Eduard Eiben
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  2. Diptapriyo Majumdar
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  3. M. S. Ramanujan
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Corresponding author

Correspondence to Diptapriyo Majumdar .

Editor information

Editors and Affiliations

  1. University of Ioannina, Ioannina, Greece

    Michael A. Bekos

  2. Universität Tübingen, Tübingen, Germany

    Michael Kaufmann

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Eiben, E., Majumdar, D., Ramanujan, M.S. (2022). On the Lossy Kernelization for Connected Treedepth Deletion Set. In: Bekos, M.A., Kaufmann, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 2022. Lecture Notes in Computer Science, vol 13453. Springer, Cham. https://doi.org/10.1007/978-3-031-15914-5_15

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  • DOI: https://doi.org/10.1007/978-3-031-15914-5_15

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  • Online ISBN: 978-3-031-15914-5

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