A Decade of Metric Differential Privacy: Advancements and Applications

Metric Differential Privacy (mDP) builds upon the core principles of Differential Privacy (DP) by incorporating various distance metrics, which offer adaptable and context-sensitive privacy guarantees for a wide range of applications, such as location-based services, text analysis, and image processing. Since its inception in 2013, mDP has garnered substantial research attention, advancing theoretical foundations, algorithm design, and practical implementations. Despite this progress, existing surveys mainly focus on traditional DP and local DP, and they provide limited coverage of mDP. This paper provides a comprehensive survey of mDP research from 2013 to 2024, tracing its development from the foundations of DP. We categorize essential mechanisms, including Laplace, Exponential, and optimization-based approaches, and assess their strengths, limitations, and application domains. Additionally, we highlight key challenges and outline future research directions to encourage innovation and real-world adoption of mDP. This survey is designed to be a valuable resource for researchers and practitioners aiming to deepen their understanding and drive progress in mDP within the broader privacy ecosystem.