License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CPM.2020.20
URN: urn:nbn:de:0030-drops-121456
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12145/
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Koana, Tomohiro ; Froese, Vincent ; Niedermeier, Rolf

Parameterized Algorithms for Matrix Completion with Radius Constraints

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LIPIcs-CPM-2020-20.pdf (0.6 MB)

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.

BibTeX - Entry

@InProceedings{koana_et_al:LIPIcs:2020:12145,
  author =	{Tomohiro Koana and Vincent Froese and Rolf Niedermeier},
  title =	{{Parameterized Algorithms for Matrix Completion with Radius Constraints}},
  booktitle =	{31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)},
  pages =	{20:1--20:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-149-8},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{161},
  editor =	{Inge Li G{\o}rtz and Oren Weimann},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12145},
  URN =		{urn:nbn:de:0030-drops-121456},
  doi =		{10.4230/LIPIcs.CPM.2020.20},
  annote =	{Keywords: fixed-parameter tractability, consensus string problems, Closest String, Closest String with Wildcards}
}

Keywords: fixed-parameter tractability, consensus string problems, Closest String, Closest String with Wildcards
Collection: 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020)
Issue Date: 2020
Date of publication: 09.06.2020

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