Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/89384
Title: Linear sketching over F2
Authors: Kannan, Sampath
Mossel, Elchanan
Sanyal, Swagato
Yaroslavtsev, Grigory
Keywords: Linear Sketch
Streaming Algorithms
DRNTU::Science::Mathematics
Issue Date: 2018
Source: Kannan, S., Mossel, E., Sanyal, S., & Yaroslavtsev, G. (2018). Linear sketching over F2. Leibniz International Proceedings in Informatics, 102, 8-. doi:10.4230/LIPIcs.CCC.2018.8
Series/Report no.: Leibniz International Proceedings in Informatics
Abstract: We initiate a systematic study of linear sketching over F_2. For a given Boolean function treated as f : F_2^n -> F_2 a randomized F_2-sketch is a distribution M over d x n matrices with elements over F_2 such that Mx suffices for computing f(x) with high probability. Such sketches for d << n can be used to design small-space distributed and streaming algorithms. Motivated by these applications we study a connection between F_2-sketching and a two-player one-way communication game for the corresponding XOR-function. We conjecture that F_2-sketching is optimal for this communication game. Our results confirm this conjecture for multiple important classes of functions: 1) low-degree F_2-polynomials, 2) functions with sparse Fourier spectrum, 3) most symmetric functions, 4) recursive majority function. These results rely on a new structural theorem that shows that F_2-sketching is optimal (up to constant factors) for uniformly distributed inputs. Furthermore, we show that (non-uniform) streaming algorithms that have to process random updates over F_2 can be constructed as F_2-sketches for the uniform distribution. In contrast with the previous work of Li, Nguyen and Woodruff (STOC'14) who show an analogous result for linear sketches over integers in the adversarial setting our result does not require the stream length to be triply exponential in n and holds for streams of length O(n) constructed through uniformly random updates.
URI: https://hdl.handle.net/10356/89384
http://hdl.handle.net/10220/46215
DOI: 10.4230/LIPIcs.CCC.2018.8
Rights: © 2018 Sampath Kannan, Elchanan Mossel, Swagato Sanyal, and Grigory Yaroslavtsev; licensed under Creative Commons License CC-BY.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

Files in This Item:
File Description SizeFormat 
Linear Sketching over F_2.pdf796.91 kBAdobe PDFThumbnail
View/Open

SCOPUSTM   
Citations 20

5
checked on Aug 31, 2020

WEB OF SCIENCETM
Citations 20

2
checked on Oct 18, 2020

Page view(s) 20

51
checked on Oct 21, 2020

Download(s) 20

26
checked on Oct 21, 2020

Google ScholarTM

Check

Altmetric


Plumx

Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.