Chakraborty, D. orcid.org/0000-0003-0534-6417, Chandran, L.S., Padinhatteeri, S. et al. (1 more author) (2023) s-Club Cluster Vertex Deletion on interval and well-partitioned chordal graphs. Discrete Applied Mathematics, 345. pp. 170-189. ISSN 0166-218X
Abstract
In this paper, we study the computational complexity of s-Club Cluster Vertex Deletion. Given a graph, s-Club Cluster Vertex Deletion (s-CVD) aims to delete the minimum number of vertices from the graph so that each connected component of the resulting graph has a diameter at most s. When s = 1, the corresponding problem is popularly known as Cluster Vertex Deletion (CVD). We provide a faster algorithm for s-CVD on interval graphs. For each s ≥ 1, we give an O (n (n + m))-time algorithm for s-CVD on interval graphs with n vertices and m edges. In the case of s = 1, our algorithm is a slight improvement over the O (n³)-time algorithm of Cao et al. (2018), and for s ≥ 2, it significantly improves the state-of-the-art running time (O (n⁴)).
We also give a polynomial-time algorithm to solve CVD on well-partitioned chordal graphs, a graph class introduced by Ahn et al. (WG 2020) as a tool for narrowing down complexity gaps for problems that are hard on chordal graphs, and easy on split graphs. Our algorithm relies on a characterisation of the optimal solution and on solving polynomially many instances of the Weighted Bipartite Vertex Cover. This generalises a result of Cao et al. (2018) on split graphs. We also show that for any even integer s ≥ 2, s-CVD is NP-hard on well-partitioned chordal graphs.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2023 Published by Elsevier B.V. This is an open access article under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Vertex deletion problem; Cluster Vertex Deletion; s-Club Cluster Vertex Deletion; Well-partitioned chordal graphs; Interval graphs |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 01 Dec 2023 15:24 |
Last Modified: | 19 Dec 2023 16:42 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.dam.2023.11.048 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:206098 |