Optimality of Linear Sketching under Modular Updates

09/24/2018

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by   Kaave Hosseini, et al.

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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 Ω(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 > 2, and to approximation instead of exact computation.