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

Authors Eduard Eiben , Robert Ganian , Iyad Kanj , Sebastian Ordyniak , Stefan Szeider

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Author Details

Eduard Eiben
  • Department of Computer Science, Royal Holloway, University of London, Egham, UK
Robert Ganian
  • Algorithms and Complexity Group, TU Wien, Austria
Iyad Kanj
  • School of Computing, DePaul University, Chicago, IL, USA
Sebastian Ordyniak
  • School of Computing, University of Leeds, UK
Stefan Szeider
  • Algorithms and Complexity Group, TU Wien, Austria

Funding

  • Ganian, Robert: Robert Ganian acknowledges support from Project No. Y1329 of the Austrian Science Fund (FWF).
  • Kanj, Iyad: Iyad Kanj acknowledges support from DePaul University through URC grant 602061.
  • Ordyniak, Sebastian: Project EP/V00252X/1 of the Engineering and Physical Sciences Research Council (EPSRC).
  • Szeider, Stefan: Stefan Szeider acknowledges support from Project No. P36420 of the Austrian Science Fund (FWF).

Cite AsGet BibTex

Eduard Eiben, Robert Ganian, Iyad Kanj, Sebastian Ordyniak, and Stefan Szeider. From Data Completion to Problems on Hypercubes: A Parameterized Analysis of the Independent Set Problem. In 18th International Symposium on Parameterized and Exact Computation (IPEC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 285, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.IPEC.2023.16

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
Keywords
  • Independent Set
  • Powers of Hypercubes
  • Diversity
  • Parameterized Complexity
  • Incomplete Data

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