NDLI: Approximation and streaming algorithms for histogram construction problems

Content Provider	ACM Digital Library
Author	Koudas, Nick Guha, Sudipto Shim, Kyuseok
Copyright Year	2006
Abstract	Histograms and related synopsis structures are popular techniques for approximating data distributions. These have been successful in query optimization and a variety of applications, including approximate querying, similarity searching, and data mining, to name a few. Histograms were a few of the earliest synopsis structures proposed and continue to be used widely. The histogram construction problem is to construct the best histogram restricted to a space bound that reflects the data distribution most accurately under a given error measure.The histograms are used as quick and easy estimates. Thus, a slight loss of accuracy, compared to the optimal histogram under the given error measure, can be offset by fast histogram construction algorithms. A natural question arises in this context: Can we find a fast near optimal approximation algorithm for the histogram construction problem? In this article, we give the first linear time (1+ε)-factor approximation algorithms (for any ε > 0) for a large number of histogram construction problems including the use of piecewise small degree polynomials to approximate data, workloads, etc. Several of our algorithms extend to data streams.Using synthetic and real-life data sets, we demonstrate that in many scenarios the approximate histograms are almost identical to optimal histograms in quality and are significantly faster to construct.
Starting Page	396
Ending Page	438
Page Count	43
File Format	PDF
ISSN	03625915
e-ISSN	15574644
DOI	10.1145/1132863.1132873
Volume Number	31
Issue Number	1
Journal	ACM Transactions on Database Systems (TODS)
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2006-03-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Data Streams Approximation algorithm Histograms
Content Type	Text
Resource Type	Article
Subject	Information Systems

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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
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