A Framework for Adversarial Streaming via Differential Privacy and Difference Estimators

Abstract

Streaming algorithms are algorithms for processing large data streams, using only a limited amount of memory. Classical streaming algorithms operate under the assumption that the input stream is fixed in advance. Recently, there is a growing interest in studying streaming algorithms that provide provable guarantees even when the input stream is chosen by an adaptive adversary. Such streaming algorithms are said to be adversarially-robust. We propose a novel framework for adversarial streaming that hybrids two recently suggested frameworks by Hassidim et al. (2020) and by Woodruff and Zhou (2021). These recently suggested frameworks rely on very different ideas, each with its own strengths and weaknesses. We combine these two frameworks (in a nontrivial way) into a single hybrid framework that gains from both approaches to obtain superior performances for turnstile streams.

A Framework for Adversarially Robust Streaming Algorithms

“…Interestingly, the way they achieve this leads them to a new class of (classical) streaming algorithms they call difference estimators, which turn out to be useful also in the sliding window (classical) model. Subsequently, [7] combined the differential privacy based techniques of [31] with the difference estimators of [53] to obtain a "best of both worlds" result with improved bounds for turnstile streams.…”

“…The space requirement of the algorithm is optimal for algorithms with such failure probability δ , which follows by an Ω(ε −2 log n log δ −1 ) lower bound for turnstile algorithms [36], where the hard instance in question has small F p flip number. 7 Theorem 4.3 (F p -estimation for λ-flip Number Turnstile Streams). Let S λ be the set of all turnstile streams with F p flip number at most λ ≥ λ ε,m ( • p p ) for any 0 < p ≤ 2.…”