Nearly Tight Bounds For Differentially Private Min s-t and Multiway Cut
CoRR(2023)
摘要
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.
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