Data privacy has become one of the most important concerns in the big data era. Because of its broad applications in machine learning and data analysis, many algorithms and theoretical results have been established for privacy clustering problems, such as k-means and k-median problems with privacy protection. However, there is little work on privacy protection in k-center clustering. Our research focuses on the k-center problem, its distributed variant, and the distributed k-center problem under differential privacy constraints. These problems model the concept of safeguarding the privacy of individual input elements, with the integration of differential privacy aimed at ensuring the security of individual information during data processing and analysis. We propose three approximation algorithms for these problems, respectively, and achieve a constant factor approximation ratio.

数据隐私已成为大数据时代最重要的问题之一。由于其在机器学习和数据分析中的广泛应用，针对隐私聚类问题已经建立了许多算法和理论成果，例如隐私保护的k均值和k中值问题。然而， k中心聚类中隐私保护方面的工作却很少。我们的研究重点是k中心问题、其分布式变体以及差分隐私约束下的分布式k中心问题。这些问题模拟了保护个人输入元素隐私的概念，并融合差异隐私，旨在确保数据处理和分析过程中个人信息的安全。我们分别针对这些问题提出了三种近似算法，并实现了恒定因子近似率。