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Computational Hardness of Private Coreset

Authors Badih Ghazi , Cristóbal Guzmán , Pritish Kamath , Alexander Knop , Ravi Kumar , Pasin Manurangsi

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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational complexity and cryptography
  • Security and privacy
Keywords
  • Differentially Private Clustering
  • Coreset
  • Cryptographic Hardness

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Abstract

We study the problem of differentially private (DP) computation of coreset for the k-means objective. For a given input set of points, a coreset is another set of points such that the k-means objective for any candidate solution is preserved up to a multiplicative (1 ± α) factor (and some additive factor). 
We prove the first computational lower bounds for this problem. Specifically, assuming the existence of one-way functions, we show that no polynomial-time (ε, 1/n^{ω(1)})-DP algorithm can compute a coreset for k-means in the 𝓁_∞-metric for some constant α > 0 (and some constant additive factor), even for k = 3. For k-means in the Euclidean metric, we show a similar result but only for α = Θ(1/d²), where d is the dimension.

Cite As Get BibTex

Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Alexander Knop, Ravi Kumar, and Pasin Manurangsi. Computational Hardness of Private Coreset. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.FORC.2026.1

Author Details

Badih Ghazi
  • Google Research, Mountain View, CA, USA
Cristóbal Guzmán
  • Pontificia Universidad Católica de Chile, Santiago, Chile
Pritish Kamath
  • Google Research, Mountain View, CA, USA
Alexander Knop
  • Google Research, Mountain View, CA, USA
Ravi Kumar
  • Google Research, Mountain View, CA, USA
Pasin Manurangsi
  • Google Research, Bangkok, Thailand

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