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Approximate sorting of data streams with limited storage

Farnoud (Hassanzadeh), Farzad and Yaakobi, Eitan and Bruck, Jehoshua (2016) Approximate sorting of data streams with limited storage. Journal of Combination Optimization, 32 (4). pp. 1133-1164. ISSN 1382-6905. doi:10.1007/s10878-015-9930-6. https://resolver.caltech.edu/CaltechAUTHORS:20161202-085415227

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Abstract

We consider the problem of approximate sorting of a data stream (in one pass) with limited internal storage where the goal is not to rearrange data but to output a permutation that reflects the ordering of the elements of the data stream as closely as possible. Our main objective is to study the relationship between the quality of the sorting and the amount of available storage. To measure quality, we use permutation distortion metrics, namely the Kendall tau, Chebyshev, and weighted Kendall metrics, as well as mutual information, between the output permutation and the true ordering of data elements. We provide bounds on the performance of algorithms with limited storage and present a simple algorithm that asymptotically requires a constant factor as much storage as an optimal algorithm in terms of mutual information and average Kendall tau distortion. We also study the case in which only information about the most recent elements of the stream is available. This setting has applications to learning user preference rankings in services such as Netflix, where items are presented to the user one at a time.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s10878-015-9930-6DOIArticle
http://link.springer.com/article/10.1007%2Fs10878-015-9930-6PublisherArticle
http://resolver.caltech.edu/CaltechAUTHORS:20141203-103210856Related ItemConference Proceeding
ORCID:
AuthorORCID
Farnoud (Hassanzadeh), Farzad0000-0002-8684-4487
Yaakobi, Eitan0000-0002-9851-5234
Bruck, Jehoshua0000-0001-8474-0812
Additional Information:© 2015 Springer Science+Business Media New York. First Online: 28 August 2015.
Subject Keywords:Approximate sorting; Data stream; Limited storage; Permutation distortion metrics; Weighted Kendall distortion; User preference ranking
Issue or Number:4
DOI:10.1007/s10878-015-9930-6
Record Number:CaltechAUTHORS:20161202-085415227
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161202-085415227
Official Citation:Farnoud, F., Yaakobi, E. & Bruck, J. J Comb Optim (2016) 32: 1133. doi:10.1007/s10878-015-9930-6
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72518
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:02 Dec 2016 22:52
Last Modified:11 Nov 2021 05:02

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