Bergougnoux, B, Eiben, E, Ganian, R et al. (2 more authors) (2021) Towards a Polynomial Kernel for Directed Feedback Vertex Set. Algorithmica, 83. pp. 1201-1221. ISSN 0178-4617
Abstract
In the DIRECTED FEEDBACK VERTEX SET (DFVS) problem, the input is a directed graph D and an integer k. The objective is to determine whether there exists a set of at most k vertices intersecting every directed cycle of D. DFVS was shown to be fixed-parameter tractable when parameterized by solution size by Chen et al. (J ACM 55(5):177–186, 2008); since then, the existence of a polynomial kernel for this problem has become one of the largest open problems in the area of parameterized algorithmics. Since this problem has remained open in spite of the best efforts of a number of prominent researchers and pioneers in the field, a natural step forward is to study the kernelization complexity of DFVS parameterized by a natural larger parameter. In this paper, we study DFVS parameterized by the feedback vertex set number of the underlying undirected graph. We provide two main contributions: a polynomial kernel for this problem on general instances, and a linear kernel for the case where the input digraph is embeddable on a surface of bounded genus.
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Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
Keywords: | Parameterized algorithms; Kernelization; (Directed) feedback vertex set |
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: | 12 Nov 2020 16:25 |
Last Modified: | 28 Apr 2021 08:06 |
Status: | Published |
Publisher: | Springer |
Identification Number: | 10.1007/s00453-020-00777-5 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:167891 |
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