Differentially Private Maximum Consensus: Design, Analysis and Impossibility Result

In network systems, calculating maximum element plays a fundamental role for distributed data analysis. Maximum consensus algorithm can accomplish the calculation in a fully distributed way. However, the data for communication are privacy-sensitive in many scenarios, making nodes unwilling to participate in the distributed calculation process. How to ensure privacy and accuracy for distributed calculation of maximum element is essential while challenging. In this paper, we first prove that exact maximum consensus and differential privacy cannot be guaranteed simultaneously. Then, to provide sufficient privacy preservation for nodes, we propose a novel differentially private maximum consensus (DPMC) algorithm where nodes perturb their initial states with Laplacian noises. We prove that DPMC algorithm preserves differential privacy and give the analytical expression of privacy preserving degree. Furthermore, the proposed algorithm also guarantees finite-time convergence and achieves high convergence accuracy. The performance tradeoff is finally analyzed and evaluated by extensive numerical simulations.