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.APPROX/RANDOM.2020.32
URN: urn:nbn:de:0030-drops-126355
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12635/
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Fomin, Fedor V. ; Golovach, Petr A. ; Panolan, Fahad ; Simonov, Kirill

Low-Rank Binary Matrix Approximation in Column-Sum Norm

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LIPIcs-APPROX32.pdf (0.7 MB)


Abstract

We consider 𝓁₁-Rank-r Approximation over {GF}(2), where for a binary m× n matrix 𝐀 and a positive integer constant r, one seeks a binary matrix 𝐁 of rank at most r, minimizing the column-sum norm ‖ 𝐀 -𝐁‖₁. We show that for every ε ∈ (0, 1), there is a {randomized} (1+ε)-approximation algorithm for 𝓁₁-Rank-r Approximation over {GF}(2) of running time m^{O(1)}n^{O(2^{4r}⋅ ε^{-4})}. This is the first polynomial time approximation scheme (PTAS) for this problem.

BibTeX - Entry

@InProceedings{fomin_et_al:LIPIcs:2020:12635,
  author =	{Fedor V. Fomin and Petr A. Golovach and Fahad Panolan and Kirill Simonov},
  title =	{{Low-Rank Binary Matrix Approximation in Column-Sum Norm}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{32:1--32:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Jaros{\l}aw Byrka and Raghu Meka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/12635},
  URN =		{urn:nbn:de:0030-drops-126355},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.32},
  annote =	{Keywords: Binary Matrix Factorization, PTAS, Column-sum norm}
}

Keywords: Binary Matrix Factorization, PTAS, Column-sum norm
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)
Issue Date: 2020
Date of publication: 11.08.2020


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