Chakraborty, D and Chandran, LS and Padinhatteeri, S and Pillai, RR (2024) s-Club Cluster Vertex Deletion on interval and well-partitioned chordal graphs. In: Discrete Applied Mathematics, 345 (345). pp. 170-189.
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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 On4. 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. © 2023
| Item Type: | Journal Article |
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| Publication: | Discrete Applied Mathematics |
| Publisher: | Elsevier B.V. |
| Additional Information: | The copyright for this article belongs to authors. |
| Keywords: | Graph algorithms; Graphic methods, Chordal graphs; CLUSTER VERTEX DELETION; Connected component; Fast algorithms; Interval graph; S-CLUB CLUSTER VERTEX DELETION; Splits graphs; Time algorithms; Vertex deletion problems; Well-partitioned chordal graph, Polynomial approximation |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 29 Feb 2024 10:59 |
| Last Modified: | 29 Feb 2024 10:59 |
| URI: | https://eprints.iisc.ac.in/id/eprint/83883 |
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