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: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/12635/
Fomin, Fedor V. ;
Golovach, Petr A. ;
Panolan, Fahad ;
Simonov, Kirill
Low-Rank Binary Matrix Approximation in Column-Sum Norm
Abstract
We consider ?₁-Rank-r Approximation over {GF}(2), where for a binary m× n matrix ? and a positive integer constant r, one seeks a binary matrix ? of rank at most r, minimizing the column-sum norm ‖ ? -?‖₁. We show that for every ε ∈ (0, 1), there is a {randomized} (1+ε)-approximation algorithm for ?₁-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}
}
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Keywords: |
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Binary Matrix Factorization, PTAS, Column-sum norm |
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Collection: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020) |
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Issue Date: |
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2020 |
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Date of publication: |
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11.08.2020 |
