  We introduce an $(\epsilon, \delta)$-jointly differentially private algorithm
for packing problems. Our algorithm not only achieves the optimal trade-off
between the privacy parameter $\epsilon$ and the minimum supply requirement (up
to logarithmic factors), but is also scalable in the sense that the running
time is linear in the number of agents $n$. Previous algorithms either run in
cubic time in $n$, or require a minimum supply per resource that is $\sqrt{n}$
times larger than the best possible.
