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Maximal "all zeros" submatrix of a sparse binary matrix

Let $A\in\left\{ 0,1\right\} ^{M\times N}$, where each row of $A$ has at most $d$ components equal to $1$, and $d\leq M\ll N\ll Md$. Question: $\forall n\leq N$, what is $m\left(n\right)$, the ...
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