Aute, S. and Panolan, F. orcid.org/0000-0001-6213-8687 (2024) Parameterized Algorithms for Minimum Sum Vertex Cover. In: Soto, J.A. and Wiese, A., (eds.) LATIN 2024: Theoretical Informatics 16th Latin American Symposium, Puerto Varas, Chile, March 18–22, 2024, Proceedings, Part II. LATIN 2024: Latin American Symposium on Theoretical Informatics, 18-22 Mar 2024, Puerto Varas, Chile. Lecture Notes in Computer Science, 14579 . Springer , pp. 193-207. ISBN 978-3-031-55601-2
Abstract
Minimum sum vertex cover of an n-vertex graph G is a bijection φ : V(G) → [n] that minimizes the cost ∑{u,v}ϵE(G) min{φ(u), φ(v)}. Finding a minimum sum vertex cover of a graph (the MSVC problem) is NP-hard. MSVC is studied well in the realm of approximation algorithms. The best-known approximation factor in polynomial time for the problem is 16/9 [Bansal, Batra, Farhadi, and Tetali, SODA 2021]. Recently, Stankovic [APPROX/RANDOM 2022] proved that achieving an approximation ratio better than 1.014 for MSVC is NP-hard, assuming the Unique Games Conjecture. We study the MSVC problem from the perspective of parameterized algorithms. The parameters we consider are the size of a minimum vertex cover and the size of a minimum clique modulator of the input graph. We obtain the following results.
- MSVC can be solved in 2²O(k) nO(1) time, where k is the size of a minimum vertex cover.
- MSVC can be solved in f(k) · nnO(1) time for some computable function f, where k is the size of a minimum clique modulator.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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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/10.1007/978-3-031-55601-2_13 |
Keywords: | FPT ;Vertex Cover; Integer Quadratic Programming |
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 15:07 |
Last Modified: | 06 Mar 2025 01:13 |
Published Version: | https://doi.org/10.1007/978-3-031-55601-2 |
Status: | Published |
Publisher: | Springer |
Series Name: | Lecture Notes in Computer Science |
Identification Number: | 10.1007/978-3-031-55601-2_13 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:208305 |