Gowda, K.N., Lonkar, A., Panolan, F. orcid.org/0000-0001-6213-8687 et al. (2 more authors) (2024) Improved FPT Algorithms for Deletion to Forest-like Structures. Algorithmica. ISSN 0178-4617
Abstract
The FEEDBACK VERTEX SET problem is undoubtedly one of the most well-studied problems in Parameterized Complexity. In this problem, given an undirected graph G and a non-negative integer k, the objective is to test whether there exists a subset S ⊆ V(G) of size at most k such that G − S is a forest. After a long line of improvement, recently, Li and Nederlof [TALG, 2022] designed a randomized algorithm for the problem running in time (O*2.7ᵏ). In the Parameterized Complexity literature, several problems around FEEDBACK VERTEX SET have been studied. Some of these include INDEPENDENT FEEDBACK VERTEX SET (where the set S should be an independent set in G), ALMOST FOREST DELETION and PSEUDOFOREST DELETION. In PSEUDOFOREST DELETION, each connected component in G − S has at most one cycle in it. However, in ALMOST FOREST DELETION, the input is a graph G and non-negative integers k, ℓ ∈ N, and the objective is to test whether there exists a vertex subset S of size at most k, such that G − S is ℓ edges away from a forest. In this paper, using the methodology of Li and Nederlof [TALG, 2022], we obtain the current fastest algorithms for all these problems. In particular we obtain the following randomized algorithms.
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s). This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use (https://www.springernature.com/gp/open-research/policies/accepted-manuscript-terms), but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00453-023-01206-z. |
Keywords: | Parameterized complexity; Independent feedback vertex set; Pseudo forest; Almost forest; Cut and count; Treewidth |
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: | 26 Jan 2024 10:54 |
Last Modified: | 09 Feb 2024 16:57 |
Status: | Published online |
Publisher: | Springer |
Identification Number: | https://doi.org/10.1007/s00453-023-01206-z |
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