Optimality of Linear Sketching under Modular Updates

Kaave Hosseini; Shachar Lovett; Grigory Yaroslavtsev

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arXiv · 1809.09063

Optimality of Linear Sketching under Modular Updates

Kaave Hosseini·Shachar Lovett·Grigory Yaroslavtsev

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Abstract

We study the relation between streaming algorithms and linear sketching algorithms, in the context of binary updates. We show that for inputs in $n$ dimensions, the existence of efficient streaming algorithms which can process $\Omega(n^2)$ updates implies efficient linear sketching algorithms with comparable cost. This improves upon the previous work of Li, Nguyen and Woodruff [LNW14] and Ai, Hu, Li and Woodruff [AHLW16] which required a triple-exponential number of updates to achieve a similar result for updates over integers. We extend our results to updates modulo $p$ for integers $p \ge 2$, and to approximation instead of exact computation.

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BibTeX RIS

Kaave Hosseini, Shachar Lovett, Grigory Yaroslavtsev. 2018-09-24. Optimality of Linear Sketching under Modular Updates. https://arxiv.org/abs/1809.09063

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