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How can we tighten the bounds of the $\ell_1$-norm of $\mathbf{A}x$ where $\mathbf{A}\in\mathbb{Z}^{m\times p}$ and $x \in \{0,1\}^p$?

I am curious about the upper bound of $\|\mathbf{A}x\|_1$ where $\mathbf{A}\in\mathbb{Z}^{m\times p}$ and $x \in \{0,1\}^p$, for a specific $\mathbf{A}$ as defined below. I know this is an NP-hard ...
Rhidya Rao's user avatar