Nearly Tight Bounds For Differentially Private Multiway Cut

Published: 21 Sept 2023, Last Modified: 02 Nov 2023NeurIPS 2023 oralEveryoneRevisionsBibTeX
Keywords: Differential Privacy, clustering, multiway cut, min cut, graph partitioning
TL;DR: We provide the first DP algorithm for min s-t cut and multiway k cut.
Abstract: Finding min $s$-$t$ cuts in graphs is a basic algorithmic tool, with applications in image segmentation, community detection, reinforcement learning, and data clustering. In this problem, we are given two nodes as terminals and the goal is to remove the smallest number of edges from the graph so that these two terminals are disconnected. We study the complexity of differential privacy for the min $s$-$t$ cut problem and show nearly tight lower and upper bounds where we achieve privacy at no cost for running time efficiency. We also develop a differentially private algorithm for the multiway $k$-cut problem, in which we are given $k$ nodes as terminals that we would like to disconnect. As a function of $k$, we obtain privacy guarantees that are exponentially more efficient than applying the advanced composition theorem to known algorithms for multiway $k$-cut. Finally, we empirically evaluate the approximation of our differentially private min $s$-$t$ cut algorithm and show that it almost matches the quality of the output of non-private ones.
Supplementary Material: pdf
Submission Number: 6725