Fast and Private Max-Sum Diversification

2026-07-19

AI Summary

This work introduces differential privacy into the Maximum Sum Dispersion (MSD) problem for the first time, proposing private algorithms that balance utility and efficiency under cardinality and matroid constraints. By integrating differential privacy mechanisms with submodular optimization and combinatorial constraint techniques, and by designing an efficient greedy strategy, the proposed method achieves near-optimal utility under strong privacy guarantees while outperforming existing non-private algorithms in runtime. Experimental results on real-world datasets demonstrate that the algorithm significantly improves computational efficiency under cardinality constraints while maintaining utility close to that of non-private baselines.

Abstract

Result diversification is crucial for generating informative, non-redundant data summaries and query outputs. Although its various formulations have been extensively studied across an array of data-driven disciplines, existing methods fail to address the privacy concerns that arise when the underlying data is sensitive. In this work, we initiate the study of result diversification under differential privacy, focusing on the max-sum diversification (MSD) problem, a widely adopted model with the objective of maximizing a linear combination of a submodular function, quantifying relevance, and the sum of pairwise distances between selected items, quantifying diversity. We propose differentially private algorithms for MSD under both cardinality and matroid constraints, achieving nearly optimal utility guarantees. At the same time, we design more efficient algorithms that maintain strong guarantees. Notably, the proposed algorithms are faster than existing non-private methods, making them appealing even in non-private settings. Experimental evaluations on real-world datasets demonstrate that the proposed approach achieves utility comparable to that of non-private baselines even under strong privacy guarantees, and significantly improves execution times for cardinality constraints.

Problem

• result diversification
• differential privacy
• max-sum diversification
• sensitive data
• privacy-preserving

Innovation

• differential privacy
• max-sum diversification
• submodular optimization
• efficient algorithms
• result diversification