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Optimal lower bounds for universal relation, and for samplers and finding duplicates in streams
, Article Annual Symposium on Foundations of Computer Science - Proceedings, 15 October 2017 through 17 October 2017 ; Volume 2017-October , 2017 , Pages 475-486 ; 02725428 (ISSN) ; 9781538634646 (ISBN) ; Nelson, J ; Pachocki, J ; Wang, Z ; Woodruff, D. P ; Yahyazadeh, M ; Sharif University of Technology
Abstract
In the communication problem UR (universal relation), Alice and Bob respectively receive x, y {0,1}^n with the promise that xy. The last player to receive a message must output an index i such that x-iy-i. We prove that the randomized one-way communication complexity of this problem in the public coin model is exactly Θ(min{n,log(1/Δ)log^2(rac n{log(1/Δ)})}) for failure probability Δ. Our lower bound holds even if promised mathop{support}(y)mathop{support}(x). As a corollary, we obtain optimal lower bounds for -p-sampling in strict turnstile streams for 0le p streams for 0 ≤ p © 2017 IEEE