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arXiv · 1904.06141

Low-rank binary matrix approximation in column-sum norm

Fedor V. Fomin·Petr A. Golovach·Fahad Panolan·Kirill Simonov
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Abstract

We consider $\ell_1$-Rank-$r$ Approximation over GF(2), where for a binary $m\times n$ matrix ${\bf A}$ and a positive integer $r$, one seeks a binary matrix ${\bf B}$ of rank at most $r$, minimizing the column-sum norm $||{\bf A} -{\bf B}||_1$. We show that for every $\varepsilon\in (0, 1)$, there is a randomized $(1+\varepsilon)$-approximation algorithm for $\ell_1$-Rank-$r$ Approximation over GF(2) of running time $m^{O(1)}n^{O(2^{4r}\cdot \varepsilon^{-4})}$. This is the first polynomial time approximation scheme (PTAS) for this problem.

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Fedor V. Fomin, Petr A. Golovach, Fahad Panolan, Kirill Simonov. 2019-04-12. Low-rank binary matrix approximation in column-sum norm. https://arxiv.org/abs/1904.06141

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