# $n$-VDD: Location Privacy Protection Based on Voronoi-Delaunay Duality

## TL;DR

This paper introduces a geometric framework using Voronoi-Delaunay duality to enhance location privacy in location-based services by hiding user locations within irregular Voronoi cells and intersection zones.

## Contribution

It presents a novel geometric approach based on Voronoi-Delaunay duality for location privacy protection, introducing multiple anonymizing models with efficient linear computations.

## Key findings

- The framework effectively conceals user locations.
- The methods are computationally efficient due to linear line intersections.
- Experiments demonstrate the approach's efficacy across various parameters.

## Abstract

To date, location privacy protection is a critical issue in Location-Based Services (LBS). In this work, we propose a novel geometric framework based on the classical discrete geometric structure, the Voronoi-Delaunay duality (VDD). We utilize the fact that the user location cannot be recovered if only given an irregular $n$-sided Voronoi cell around it, and the anonymity zone is the intersection of all the parallel strips perpendicular to and bounded by $n$ Voronoi edges. The irregular Voronoi cell and its variations can be used as the concealing space to hide the user location or the region of interest and submitted to the LBS server. Within this framework, we propose multiple typical anonymizing models by introducing irregularity to the convex regular VDD structure by shifting the interior Voronoi cell, exterior Delaunay polygon, sector rays, or their combinations. The proposed methods are efficient by taking advantage of the VDD principle where main computations are linear line-line intersections. Experiments with various parameters demonstrate the efficiency and efficacy of the proposed $n$-VDD framework.