# Scalable and Jointly Differentially Private Packing

## TL;DR

This paper presents a scalable, jointly differentially private algorithm for packing problems that optimally balances privacy and supply requirements, with linear runtime in the number of agents.

## Contribution

It introduces a new $(\epsilon,\delta)$-jointly differentially private algorithm that is both scalable and achieves near-optimal privacy-supply trade-offs.

## Key findings

- Achieves optimal privacy-supply trade-off up to logarithmic factors.
- Runs in linear time relative to the number of agents.
- Outperforms previous algorithms with cubic time or larger supply requirements.

## Abstract

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.