License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CCC.2019.13
URN: urn:nbn:de:0030-drops-108355
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10835/
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Hosseini, Kaave ; Lovett, Shachar ; Yaroslavtsev, Grigory

Optimality of Linear Sketching Under Modular Updates

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LIPIcs-CCC-2019-13.pdf (0.6 MB)

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 [Yi Li et al., 2014] and Ai, Hu, Li and Woodruff [Yuqing Ai et al., 2016] 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.

BibTeX - Entry

@InProceedings{hosseini_et_al:LIPIcs:2019:10835,
  author =	{Kaave Hosseini and Shachar Lovett and Grigory Yaroslavtsev},
  title =	{{Optimality of Linear Sketching Under Modular Updates}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{13:1--13:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Amir Shpilka},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10835},
  URN =		{urn:nbn:de:0030-drops-108355},
  doi =		{10.4230/LIPIcs.CCC.2019.13},
  annote =	{Keywords: communication complexity, linear sketching, streaming algorithm}
}

Keywords: communication complexity, linear sketching, streaming algorithm
Collection: 34th Computational Complexity Conference (CCC 2019)
Issue Date: 2019
Date of publication: 16.07.2019

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