Parameterized Algorithms for Matrix Completion with Radius Constraints
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.
fixed-parameter tractability
consensus string problems
Closest String
Closest String with Wildcards
Theory of computation~Parameterized complexity and exact algorithms
Theory of computation~Pattern matching
20:1-20:14
Regular Paper
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].
Tomohiro
Koana
Tomohiro Koana
Technische Universität Berlin, Faculty IV, Algorithmics and Computational Complexity, Germany
https://orcid.org/0000-0002-8684-0611
Partially supported by the DFG project MATE (NI 369/17).
Vincent
Froese
Vincent Froese
Technische Universität Berlin, Faculty IV, Algorithmics and Computational Complexity, Germany
Rolf
Niedermeier
Rolf Niedermeier
Technische Universität Berlin, Faculty IV, Algorithmics and Computational Complexity, Germany
https://orcid.org/0000-0003-1703-1236
10.4230/LIPIcs.CPM.2020.20
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Tomohiro Koana, Vincent Froese, and Rolf Niedermeier
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