Low-rank binary matrix approximation in column-sum norm

04/12/2019

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by   Fedor V. Fomin, et al.

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We consider ℓ_1-Rank-r Approximation over GF(2), where for a binary m× n matrix A and a positive integer 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 ℓ_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.