Privacy preserving clustering with constraints

TL;DR

This paper explores how to adapt classical clustering algorithms to incorporate privacy constraints, specifically ensuring centers are only opened if enough clients are assigned, and demonstrates combining privacy with other constraints.

Contribution

It introduces methods to modify approximation algorithms for clustering to respect privacy constraints, particularly the requirement of minimum client assignments per center.

Findings

Developed techniques to incorporate privacy constraints into clustering algorithms.

Showed how to combine privacy with other constraints in clustering.

Provided theoretical foundations for privacy-preserving clustering algorithms.

Abstract

The $k$-center problem is a classical combinatorial optimization problem which asks to find $k$ centers such that the maximum distance of any input point in a set $P$ to its assigned center is minimized. The problem allows for elegant $2$-approximations. However, the situation becomes significantly more difficult when constraints are added to the problem. We raise the question whether general methods can be derived to turn an approximation algorithm for a clustering problem with some constraints into an approximation algorithm that respects one constraint more. Our constraint of choice is privacy: Here, we are asked to only open a center when at least $\ell$ clients will be assigned to it. We show how to combine privacy with several other constraints.