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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Bibliographic Details
Published in:Algorithmica Vol. 88; no. 1; p. 8
Main Authors: Eiben, Eduard, Ganian, Robert, Kanj, Iyad, Ordyniak, Sebastian, Szeider, Stefan
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2026
Springer Nature B.V
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-025-01354-4