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Subspace exploration : bounds on projected frequency estimation

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Cormode, Graham, Dickens, Charlie and Woodruff, David P. (2021) Subspace exploration : bounds on projected frequency estimation. In: The 2021 ACM SIGMOD/PODS Conference, Virtual conference, 20-25 Jun 2021. Published in: PODS'21: Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems pp. 273-284. ISBN 9781450383813. doi:10.1145/3452021.3458312

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Official URL: https://doi.org/10.1145/3452021.3458312

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Abstract

Given an n×d dimensional dataset A, a projection query specifies a subset C⊆[d] of columns which yields a new n×|C| array. We study the space complexity of computing data analysis functions over such subspaces, including heavy hitters and norms, when the subspaces are revealed only after observing the data. We show that this important class of problems is typically hard: for many problems, we show 2Ω(d) lower bounds. However, we present upper bounds which demonstrate space dependency better than 2d. That is, for c,c′∈(0,1) and a parameter N=2d an Nc-approximation can be obtained in space min(Nc′,n), showing that it is possible to improve on the naïve approach of keeping information for all 2d subsets of d columns. Our results are based on careful constructions of instances using coding theory and novel combinatorial reductions that exhibit such space-approximation tradeoffs.

Item Type: Conference Item (Paper)
Subjects: Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Divisions: Faculty of Science > Computer Science
Library of Congress Subject Headings (LCSH): Computer algorithms, Database management, Computational complexity, Querying (Computer science)
Journal or Publication Title: PODS'21: Proceedings of the 40th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems
Publisher: ACM
ISBN: 9781450383813
Official Date: 20 June 2021
Dates:
DateEvent
20 June 2021Published
20 April 2021Accepted
Page Range: pp. 273-284
DOI: 10.1145/3452021.3458312
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Open Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
ERC-2014-CoG 647557European Research Councilhttp://dx.doi.org/10.13039/501100000781
CCF-1815840National Science Foundationhttp://dx.doi.org/10.13039/501100008982
5R01HG 10798-2National Institutes of Healthhttp://dx.doi.org/10.13039/100000002
Conference Paper Type: Paper
Title of Event: The 2021 ACM SIGMOD/PODS Conference
Type of Event: Conference
Location of Event: Virtual conference
Date(s) of Event: 20-25 Jun 2021
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