From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem

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 power...

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Veröffentlicht in:	Algorithmica Jg. 88; H. 1; S. 8
Hauptverfasser:	Eiben, Eduard, Ganian, Robert, Kanj, Iyad, Ordyniak, Sebastian, Szeider, Stefan
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.02.2026 Springer Nature B.V
Schlagworte:	Algorithm Analysis and Problem Complexity Algorithms Clustering Complexity Computer Science Computer Systems Organization and Communication Networks Data science Data Structures and Information Theory Graph theory Hypercubes Machine learning Mathematics of Computing Parameterization Parameters Theory of Computation Clustering Data completion Parameterized complexity Independent set problem on hypercubes First Order Logic model checking Diversity
ISSN:	0178-4617, 1432-0541
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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 First Order Logic (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.
AbstractList	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 First Order Logic (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. 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 First Order Logic (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.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 First Order Logic (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.
ArticleNumber	8
Author	Ordyniak, Sebastian Ganian, Robert Kanj, Iyad Eiben, Eduard Szeider, Stefan
Author_xml	– sequence: 1 givenname: Eduard surname: Eiben fullname: Eiben, Eduard organization: Department of Computer Science, Royal Holloway, University of London – sequence: 2 givenname: Robert surname: Ganian fullname: Ganian, Robert organization: Algorithms and Complexity Group, TU Wien – sequence: 3 givenname: Iyad surname: Kanj fullname: Kanj, Iyad organization: School of Computing, DePaul University – sequence: 4 givenname: Sebastian surname: Ordyniak fullname: Ordyniak, Sebastian email: sordyniak@gmail.com organization: School of Computing, University of Leeds – sequence: 5 givenname: Stefan surname: Szeider fullname: Szeider, Stefan organization: Algorithms and Complexity Group, TU Wien
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SubjectTerms	Algorithm Analysis and Problem Complexity Algorithms Clustering Complexity Computer Science Computer Systems Organization and Communication Networks Data science Data Structures and Information Theory Graph theory Hypercubes Machine learning Mathematics of Computing Parameterization Parameters Theory of Computation
Title	From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem
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