NDLI: Streaming Algorithms via Precision Sampling

Content Provider	IEEE Xplore Digital Library
Author	Andoni, A. Krauthgamer, R. Onak, K.
Copyright Year	2011
Abstract	A technique introduced by Indyk and Woodruff (STOC 2005) has inspired several recent advances in data-stream algorithms. We show that a number of these results follow easily from the application of a single probabilistic method called Precision Sampling. Using this method, we obtain simple data-stream algorithms that maintain a randomized sketch of an input vector $x=(x_1,x_2,\ldots,x_n)$, which is useful for the following applications:* Estimating the $F_k$-moment of $x$, for $k>2$.* Estimating the $\ell_p$-norm of $x$, for $p\in[1,2]$, with small update time.* Estimating cascaded norms $\ell_p(\ell_q)$ for all $p,q>0$.* $\ell_1$ sampling, where the goal is to produce an element $i$ with probability (approximately) $\|x_i\|/\\|x\\|_1$. It extends to similarly defined $\ell_p$-sampling, for $p\in [1,2]$. For all these applications the algorithm is essentially the same: scale the vector $x$ entry-wise by a well-chosen random vector, and run a heavy-hitter estimation algorithm on the resulting vector. Our sketch is a linear function of $x$, thereby allowing general updates to the vector $x$. Precision Sampling itself addresses the problem of estimating a sum $\sum_{i=1}^n a_i$ from weak estimates of each real $a_i\in[0,1]$. More precisely, the estimator first chooses a desired precision$u_i\in(0,1]$ for each $i\in[n]$, and then it receives an estimate of every $a_i$ within additive $u_i$. Its goal is to provide a good approximation to $\sum a_i$ while keeping a tab on the ``approximation cost'' $\sum_i (1/u_i)$. Here we refine previous work (Andoni, Krauthgamer, and Onak, FOCS 2010)which shows that as long as $\sum a_i=\Omega(1)$, a good multiplicative approximation can be achieved using total precision of only $O(n\log n)$.
Starting Page	363
Ending Page	372
File Size	567412
Page Count	10
File Format	PDF
ISBN	9781457718434
ISSN	02725428
e-ISBN	9780769545714
DOI	10.1109/FOCS.2011.82
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-10-22
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Vectors Estimation Reactive power Approximation algorithms Approximation methods Algorithm design and analysis Random variables cascaded norms streaming sampling moments
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Libarray of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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