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A longstanding observation, which was partially proven in \cite{LNW14,AHLW16}, is that any turnstile streaming algorithm can be implemented as a linear sketch (the reverse is trivially true). We study the relationship between turnstile streaming and linear sketching algorithms in more detail, giving both new separations and new equivalences between the two models. It was shown in \cite{LNW14} that, if a turnstile algorithm works for arbitrarily long streams with arbitrarily large coordinates at intermediate stages of the stream, then the turnstile algorithm is equivalent to a linear sketch. We show separations of the opposite form: if either the stream length or the maximum value of the stream are substantially restricted, there exist problems where linear sketching is exponentially harder than turnstile streaming. A further limitation of the \cite{LNW14} equivalence is that the turnstile sketching algorithm is neither explicit nor uniform, but requires an exponentially long advice string. We show how to remove this limitation for deterministic streaming algorithms: we give an explicit small-space algorithm that takes the streaming algorithm and computes an equivalent module.
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This content will become publicly available on July 13, 2026
Maximum Coverage in Turnstile Streams with Applications to Fingerprinting Measures
In the maximum coverage problem we are given d subsets from a universe [n], and the goal is to output k subsets such that their union covers the largest possible number of distinct items. We present the first algorithm for maximum coverage in the turnstile streaming model, where updates which insert or delete an item from a subset come one-by-one. Notably our algorithm only uses polylogn update time. We also present turnstile streaming algorithms for targeted and general fingerprinting for risk management where the goal is to determine which features pose the greatest re-identification risk in a dataset. As part of our work, we give a result of independent interest: an algorithm to estimate the complement of the pth frequency moment of a vector for p ≥ 2. Empirical evaluation confirms the practicality of our fingerprinting algorithms demonstrating a speedup of up to 210x over prior work.
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- Award ID(s):
- 2311649
- PAR ID:
- 10599721
- Publisher / Repository:
- Proceedings of Machine Learning Research
- Date Published:
- ISSN:
- 2640-3498
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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