Faster Update Time for Turnstile Streaming Algorithms
Josh Alman, Huacheng Yu

TL;DR
This paper introduces a novel algorithm that significantly accelerates update times for linear sketches in turnstile streaming models, impacting various streaming applications without increasing space complexity.
Contribution
It presents the first worst-case $O( ext{polylog}(n))$ update time algorithm for maintaining linear sketches in turnstile streams, improving efficiency while preserving space bounds.
Findings
Achieves $O( ext{log}^{0.582} n)$ worst-case update time for CountSketch and CountMin sketches.
Extends to maintaining multiple sketches with bucket partitioning using limited independence hashing.
Further improves to $O( ext{log}^{0.187} n)$ update time with arbitrary word operations.
Abstract
In this paper, we present a new algorithm for maintaining linear sketches in turnstile streams with faster update time. As an application, we show that \texttt{Count} sketches or \texttt{CountMin} sketches with a constant number of columns (i.e., buckets) can be implicitly maintained in \emph{worst-case} update time using words of space, on a standard word RAM with word-size . The exponent , where is the current matrix multiplication exponent. Due to the numerous applications of linear sketches, our algorithm improves the update time for many streaming problems in turnstile streams, in the high success probability setting, without using more space, including norm estimation, heavy hitters, point query with or error, etc. Our algorithm generalizes, with the…
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Taxonomy
TopicsAlgorithms and Data Compression · Complexity and Algorithms in Graphs · Machine Learning and Algorithms
