Chakraborty, D and Chandran, LS and Padinhatteeri, S and Pillai, RR (2021) Algorithms and Complexity of s-Club Cluster Vertex Deletion. In: 32nd International Workshop on Combinatorial Algorithms, IWOCA 2021, 5-7 Jul 2021, pp. 152-164.
Full text not available from this repository.Abstract
An s-club is a graph which has diameter at most s. Let G be a graph. A set of vertices D� V(G) is an s-club deleting (s -CD) set if each connected component of G- D is an s-club. In the s -Club Cluster Vertex Deletion (s -CVD) problem, the goal is to find an s-CD set with minimum cardinality. When s= 1, the s -CVD is equivalent to the well-studied Cluster Vertex Deletion problem. On the negative side, we show that unless the Unique Games Conjecture is false, there is no (2 - ϵ) -algorithm for 2-CVD on split graphs, for any ϵ> 0. This contrast the polynomial-time solvability of Cluster Vertex Deletion on split graphs. We show that for each s� 2, s-CVD is NP-hard on bounded degree planar bipartite graphs and APX-hard on bounded degree bipartite graphs. On the positive side, we give a polynomial-time algorithm to solve s-CVD on trapezoid graphs, for each s� 1. © 2021, Springer Nature Switzerland AG.
| Item Type: | Conference Paper |
|---|---|
| Publication: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Publisher: | Springer Science and Business Media Deutschland GmbH |
| Additional Information: | The copyright for this article belongs to Springer Science and Business Media Deutschland GmbH |
| Keywords: | Graph algorithms; Graph theory; Graphic methods; NP-hard; Polynomial approximation, Algorithms and complexity; Bipartite graphs; Connected component; Polynomial-time; Polynomial-time algorithms; Trapezoid graphs; Unique games conjecture; Vertex deletion problems, Clustering algorithms |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 28 Nov 2021 09:20 |
| Last Modified: | 28 Nov 2021 09:20 |
| URI: | http://eprints.iisc.ac.in/id/eprint/69962 |
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