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A Differentially Private Approximation of the Width Problem

Authors Mor Hale , Or Sheffet

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Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Differential privacy
  • computational geometry
  • width approximation
  • private algorithms

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Abstract

The width of a point set - the minimum distance between two parallel hyperplanes enclosing the data - is a fundamental geometric measure that captures how "flat" or "fat" a dataset is. As such, it serves as a basic shape descriptor used in visualization, convex hull approximation, and geometric data analysis. Despite its importance, width is highly sensitive to single-point changes, and no differentially private algorithm for approximating it was previously known.
We present the first pure ε-differentially private algorithm that approximates the width of a dataset. Our algorithm is a private adaptation of Chan’s approximation scheme [Chan, 2000] and operates by privately approximating the solution to a collection of suitably formulated linear programs. In addition to estimating the width, our method privately identifies a corresponding direction, enabling a private "fattening" transformation of the dataset - a basic structural preprocessing step for many geometric algorithms. This work advances the understanding of how geometric shape descriptors can admit good approximations even under the constraints of differential privacy.

Cite As Get BibTex

Mor Hale and Or Sheffet. A Differentially Private Approximation of the Width Problem. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FORC.2026.18

Author Details

Mor Hale
  • Bar-Ilan University, Ramat Gan, Israel
Or Sheffet
  • Bar-Ilan University, Ramat Gan, Israel

References

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