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Finding Geometric Facilities with Location Privacy

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Abstract

We examine the problem of discovering the set P of points in a given topology that constitutes a k-median set for that topology, while maintaining location privacy. That is, there exists a set U of points in a d-dimensional topology for which a k-median set must be found by some algorithm A, without disclosing the location of points in U to the executor of A. We define a privacy preserving data model for a coordinate system we call a "Topology Descriptor Grid", and show how it can be used to find the rectilinear 1-median of the system and a constant factor approximation for the Euclidean 1-median. We achieve a constant factor approximation for the rectilinear 2-median of a grid topology. Additionally we show upper and lower bounds for the k-center problem.

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Acknowledgements

This research was (partially) funded by the Israeli Science Foundation (Grant No. 465/22), Israeli Ministry of Science (Grant No. 0005355), and by the Army Research Office under Grant Number W911NF-22-1-0225. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. The authors would like to thank the reviewers whose valuable comments greatly improved the presentation of this paper.

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  1. School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel

    Eyal Nussbaum & Michael Segal

  2. Taras Shevchenko National University, Kyiv, 01033, Ukraine

    Oles Holembovskyy

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  1. Eyal Nussbaum
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  2. Michael Segal
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Correspondence to Michael Segal.

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Nussbaum, E., Segal, M. & Holembovskyy, O. Finding Geometric Facilities with Location Privacy. Algorithmica 85, 3572–3601 (2023). https://doi.org/10.1007/s00453-023-01156-6

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