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The Cartographer
Tight Space Lower Bound for Pseudo-Deterministic Approximate Counting
April 04, 2023 Β· Declared Dead Β· π IEEE Annual Symposium on Foundations of Computer Science
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Authors
Ofer Grossman, Meghal Gupta, Mark Sellke
arXiv ID
2304.01438
Category
cs.DS: Data Structures & Algorithms
Cross-listed
cs.CC
Citations
6
Venue
IEEE Annual Symposium on Foundations of Computer Science
Last Checked
4 months ago
Abstract
We investigate one of the most basic problems in streaming algorithms: approximating the number of elements in the stream. In 1978, Morris famously gave a randomized algorithm achieving a constant-factor approximation error for streams of length at most N in space $O(\log \log N)$. We investigate the pseudo-deterministic complexity of the problem and prove a tight $Ξ©(\log N)$ lower bound, thus resolving a problem of Goldwasser-Grossman-Mohanty-Woodruff.
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