Select the maximum number of links to satisfy per-link constraint. How to prove is NP-hard?
Even when each entry of G is in {0,1}, that is W[1]-hard by reduction from independent set:

$\mathbf{G}$ ​ = ​ adjacency matrix + identity matrix ​ ​ ​ and ​ ​ ​ $\tau = 2$ ​ ​ ​ and ​ ​ ​ $0 &lt; \epsilon &lt; 1/\hspace{.02 in}2$ ​ ​ ​ .