Time lower bounds for nonadaptive turnstile streaming algorithms

TL;DR

This paper establishes the first non-trivial lower bounds on update times for non-adaptive turnstile streaming algorithms, impacting problems like heavy hitters and entropy estimation.

Contribution

It introduces the first non-trivial update time lower bounds for non-adaptive turnstile streaming algorithms, expanding understanding beyond space bounds.

Findings

Lower bounds apply to randomized and deterministic algorithms

Bounds hold for heavy hitters, point query, entropy, and moment estimation

Nearly match known upper bounds in some deterministic cases

Abstract

We say a turnstile streaming algorithm is "non-adaptive" if, during updates, the memory cells written and read depend only on the index being updated and random coins tossed at the beginning of the stream (and not on the memory contents of the algorithm). Memory cells read during queries may be decided upon adaptively. All known turnstile streaming algorithms in the literature are non-adaptive. We prove the first non-trivial update time lower bounds for both randomized and deterministic turnstile streaming algorithms, which hold when the algorithms are non-adaptive. While there has been abundant success in proving space lower bounds, there have been no non-trivial update time lower bounds in the turnstile model. Our lower bounds hold against classically studied problems such as heavy hitters, point query, entropy estimation, and moment estimation. In some cases of deterministic algorithms, our lower bounds nearly match known upper bounds.