Parameterized Algorithms for Matrix Completion with Radius Constraints

Authors Tomohiro Koana , Vincent Froese, Rolf Niedermeier



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Author Details

Tomohiro Koana
  • Technische Universität Berlin, Faculty IV, Algorithmics and Computational Complexity, Germany
Vincent Froese
  • Technische Universität Berlin, Faculty IV, Algorithmics and Computational Complexity, Germany
Rolf Niedermeier
  • Technische Universität Berlin, Faculty IV, Algorithmics and Computational Complexity, Germany

Acknowledgements

We are grateful to Christian Komusiewicz for helpful feedback on an earlier version of this work and to Stefan Szeider for pointing us to reference [Eduard Eiben et al., 2019].

Cite AsGet BibTex

Tomohiro Koana, Vincent Froese, and Rolf Niedermeier. Parameterized Algorithms for Matrix Completion with Radius Constraints. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 20:1-20:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.CPM.2020.20

Abstract

Considering matrices with missing entries, we study NP-hard matrix completion problems where the resulting completed matrix should have limited (local) radius. In the pure radius version, this means that the goal is to fill in the entries such that there exists a "center string" which has Hamming distance to all matrix rows as small as possible. In stringology, this problem is also known as Closest String with Wildcards. In the local radius version, the requested center string must be one of the rows of the completed matrix. Hermelin and Rozenberg [CPM 2014, TCS 2016] performed a parameterized complexity analysis for Closest String with Wildcards. We answer one of their open questions, fix a bug concerning a fixed-parameter tractability result in their work, and improve some running time upper bounds. For the local radius case, we reveal a computational complexity dichotomy. In general, our results indicate that, although being NP-hard as well, this variant often allows for faster (fixed-parameter) algorithms.

Subject Classification

ACM Subject Classification
  • Theory of computation → Parameterized complexity and exact algorithms
  • Theory of computation → Pattern matching
Keywords
  • fixed-parameter tractability
  • consensus string problems
  • Closest String
  • Closest String with Wildcards

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References

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