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Low-Rank Binary Matrix Approximation in Column-Sum Norm

Authors Fedor V. Fomin , Petr A. Golovach , Fahad Panolan , Kirill Simonov

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Fedor V. Fomin
  • Department of Informatics, University of Bergen, Norway
Petr A. Golovach
  • Department of Informatics, University of Bergen, Norway
Fahad Panolan
  • Department of Computer Science and Engineering, IIT Hyderabad, India
Kirill Simonov
  • Department of Informatics, University of Bergen, Norway

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Fedor V. Fomin, Petr A. Golovach, Fahad Panolan, and Kirill Simonov. Low-Rank Binary Matrix Approximation in Column-Sum Norm. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 32:1-32:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Binary Matrix Factorization
  • PTAS
  • Column-sum norm


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