Eiben, E., Ganian, R., Kanj, I. et al. (2 more authors) (2023) From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem. In: Dagstuhl Reports. 18th International Symposium on Parameterized and Exact Computation (IPEC 2023), 06-08 Sep 2023, Amsterdam, Netherlands. Leibniz International Proceedings in Informatics (LIPIcs), 285 . Schloss Dagstuhl - Leibniz-Zentrum für Informatik , Wadern, Merzig-Wadern, Saarland , 16:1-16:14. ISBN 978-3-95977-305-8
Abstract
Several works have recently investigated the parameterized complexity of data completion problems, motivated by their applications in machine learning, and clustering in particular. Interestingly, these problems can be equivalently formulated as classical graph problems on induced subgraphs of powers of partially-defined hypercubes.
In this paper, we follow up on this recent direction by investigating the Independent Set problem on this graph class, which has been studied in the data science setting under the name Diversity. We obtain a comprehensive picture of the problem’s parameterized complexity and establish its fixed-parameter tractability w.r.t. the solution size plus the power of the hypercube.
Given that several such FO-definable problems have been shown to be fixed-parameter tractable on the considered graph class, one may ask whether fixed-parameter tractability could be extended to capture all FO-definable problems. We answer this question in the negative by showing that FO model checking on induced subgraphs of hypercubes is as difficult as FO model checking on general graphs.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © Eduard Eiben, Robert Ganian, Iyad Kanj, Sebastian Ordyniak, and Stefan Szeider; licensed under Creative Commons License CC-BY 4.0. |
Keywords: | Independent Set, Powers of Hypercubes, Diversity, Parameterized Complexity, Incomplete Data |
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) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/V00252X/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 10 Aug 2023 09:20 |
Last Modified: | 12 Jan 2024 14:56 |
Published Version: | https://drops.dagstuhl.de/entities/document/10.423... |
Status: | Published |
Publisher: | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
Series Name: | Leibniz International Proceedings in Informatics (LIPIcs) |
Identification Number: | 10.4230/LIPIcs.IPEC.2023.16 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:202299 |