Improved Differentially Private Algorithms for Rank Aggregation

TL;DR

This paper advances differentially private algorithms for rank aggregation, reducing errors for Kemeny and footrule problems, and introduces near-optimal solutions with improved approximation guarantees.

Contribution

It provides improved DP PTASes for Kemeny rank aggregation and introduces the first DP algorithms for footrule rank aggregation, achieving near-optimal and 2-approximation results.

Findings

Smaller additive error in DP PTASes for Kemeny aggregation.

First DP algorithms for footrule rank aggregation.

Achieves near-optimal and 2-approximation guarantees.

Abstract

Rank aggregation is a task of combining the rankings of items from multiple users into a single ranking that best represents the users' rankings. Alabi et al. (AAAI'22) presents differentially-private (DP) polynomial-time approximation schemes (PTASes) and $5$-approximation algorithms with certain additive errors for the Kemeny rank aggregation problem in both central and local models. In this paper, we present improved DP PTASes with smaller additive error in the central model. Furthermore, we are first to study the footrule rank aggregation problem under DP. We give a near-optimal algorithm for this problem; as a corollary, this leads to 2-approximation algorithms with the same additive error as the $5$-approximation algorithms of Alabi et al. for the Kemeny rank aggregation problem in both central and local models.