TY - GEN
T1 - A Differentially Private Linear-Time fPTAS for the Minimum Enclosing Ball Problem
AU - Mahpud, Bar
AU - Sheffet, Or
N1 - Publisher Copyright: © 2022 Neural information processing systems foundation. All rights reserved.
PY - 2022
Y1 - 2022
N2 - The Minimum Enclosing Ball (MEB) problem is one of the most fundamental problems in clustering, with applications in operations research, statistics and computational geometry. In this works, we give the first linear time differentially private (DP) fPTAS for the Minimum Enclosing Ball problem, improving both on the runtime and the utility bound of the best known DP-PTAS for the problem, of Ghazi et al [21]. Given n points in Rd that are covered by the ball B(θopt, ropt), our simple iterative DP-algorithm returns a ball B(θ, r) where r ≤ (1 + γ)ropt and which leaves at most Õ((equation presented)) points uncovered in Õ(n/γ2)-time. We also give a local-model version of our algorithm, that leaves at most Õ((equation presented)) points uncovered, improving on the n0.67-bound of Nissim and Stemmer [31] (at the expense of other parameters). Lastly, we test our algorithm empirically and discuss open problems.
AB - The Minimum Enclosing Ball (MEB) problem is one of the most fundamental problems in clustering, with applications in operations research, statistics and computational geometry. In this works, we give the first linear time differentially private (DP) fPTAS for the Minimum Enclosing Ball problem, improving both on the runtime and the utility bound of the best known DP-PTAS for the problem, of Ghazi et al [21]. Given n points in Rd that are covered by the ball B(θopt, ropt), our simple iterative DP-algorithm returns a ball B(θ, r) where r ≤ (1 + γ)ropt and which leaves at most Õ((equation presented)) points uncovered in Õ(n/γ2)-time. We also give a local-model version of our algorithm, that leaves at most Õ((equation presented)) points uncovered, improving on the n0.67-bound of Nissim and Stemmer [31] (at the expense of other parameters). Lastly, we test our algorithm empirically and discuss open problems.
UR - http://www.scopus.com/inward/record.url?scp=85163182010&partnerID=8YFLogxK
M3 - منشور من مؤتمر
T3 - Advances in Neural Information Processing Systems
BT - Advances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
A2 - Koyejo, S.
A2 - Mohamed, S.
A2 - Agarwal, A.
A2 - Belgrave, D.
A2 - Cho, K.
A2 - Oh, A.
T2 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
Y2 - 28 November 2022 through 9 December 2022
ER -