## Geomasking through Perturbation, or Counting Points in Circles

Motivated by a technique in privacy protection, in which *n* points are randomly perturbed by at most a distance *r*, we study the following problem: Given *n* points and *m* circles in the plane, what is the maximum *r* such that the number of points included in each circle does not change? We also consider a more general question, where we allow the number of points included in each circle to change by a certain factor. We discuss several algorithms for the problems, analyze what parameters of the input influence their running times, and consider a special case where the circles are aligned on a grid, which has important applications.

keywords: Computational Geometry, Data Imprecision, UDG

### Workshop or Poster (weakly reviewed)

Jun Luo, Maarten Löffler, Rodrigo Silveira

Geomasking through Perturbation, or Counting Points in Circles

Proc. 33rd European Workshop on Computational Geometry

209–212, 2017

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