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  1. Transactions on Database Systems (TODS)
  2. ACM Transactions on Database Systems (TODS) : Volume 38
  3. Issue 4(Invited papers issue), November 2013
  4. Mergeable summaries
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ACM Transactions on Database Systems (TODS) : Volume 42
ACM Transactions on Database Systems (TODS) : Volume 41
ACM Transactions on Database Systems (TODS) : Volume 40
ACM Transactions on Database Systems (TODS) : Volume 39
ACM Transactions on Database Systems (TODS) : Volume 38
Issue 4(Invited papers issue), November 2013
Foreword to invited papers issue
High-performance complex event processing over hierarchical data
Consistent thinning of large geographical data for map visualization
XLynx—An FPGA-based XML filter for hybrid XQuery processing
The complexity of regular expressions and property paths in SPARQL
Static analysis and optimization of semantic web queries
Mergeable summaries
Validating XML documents in the streaming model with external memory
Learning schema mappings
Issue 3, August 2013
Issue 2, June 2013
Issue 1, April 2013
ACM Transactions on Database Systems (TODS) : Volume 37
ACM Transactions on Database Systems (TODS) : Volume 36
ACM Transactions on Database Systems (TODS) : Volume 35
ACM Transactions on Database Systems (TODS) : Volume 34
ACM Transactions on Database Systems (TODS) : Volume 33
ACM Transactions on Database Systems (TODS) : Volume 32
ACM Transactions on Database Systems (TODS) : Volume 31
ACM Transactions on Database Systems (TODS) : Volume 30
ACM Transactions on Database Systems (TODS) : Volume 29
ACM Transactions on Database Systems (TODS) : Volume 28
ACM Transactions on Database Systems (TODS) : Volume 27
ACM Transactions on Database Systems (TODS) : Volume 26
ACM Transactions on Database Systems (TODS) : Volume 25
ACM Transactions on Database Systems (TODS) : Volume 24
ACM Transactions on Database Systems (TODS) : Volume 23
ACM Transactions on Database Systems (TODS) : Volume 22
ACM Transactions on Database Systems (TODS) : Volume 21
ACM Transactions on Database Systems (TODS) : Volume 20
ACM Transactions on Database Systems (TODS) : Volume 19
ACM Transactions on Database Systems (TODS) : Volume 18
ACM Transactions on Database Systems (TODS) : Volume 17
ACM Transactions on Database Systems (TODS) : Volume 16
ACM Transactions on Database Systems (TODS) : Volume 15
ACM Transactions on Database Systems (TODS) : Volume 14
ACM Transactions on Database Systems (TODS) : Volume 13
ACM Transactions on Database Systems (TODS) : Volume 12
ACM Transactions on Database Systems (TODS) : Volume 11
ACM Transactions on Database Systems (TODS) : Volume 10
ACM Transactions on Database Systems (TODS) : Volume 9
ACM Transactions on Database Systems (TODS) : Volume 8
ACM Transactions on Database Systems (TODS) : Volume 7
ACM Transactions on Database Systems (TODS) : Volume 6
ACM Transactions on Database Systems (TODS) : Volume 5
ACM Transactions on Database Systems (TODS) : Volume 4
ACM Transactions on Database Systems (TODS) : Volume 3
ACM Transactions on Database Systems (TODS) : Volume 2
ACM Transactions on Database Systems (TODS) : Volume 1

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Mergeable summaries

Content Provider ACM Digital Library
Author Huang, Zengfeng Phillips, Jeff M. Yi, Ke Agarwal, Pankaj K. Cormode, Graham Wei, Zhewei
Copyright Year 2013
Abstract We study the $\textit{mergeability}$ of data summaries. Informally speaking, mergeability requires that, given two summaries on two datasets, there is a way to merge the two summaries into a single summary on the two datasets combined together, while preserving the error and size guarantees. This property means that the summaries can be merged in a way akin to other algebraic operators such as sum and max, which is especially useful for computing summaries on massive distributed data. Several data summaries are trivially mergeable by construction, most notably all the $\textit{sketches}$ that are linear functions of the datasets. But some other fundamental ones, like those for heavy hitters and quantiles, are not (known to be) mergeable. In this article, we demonstrate that these summaries are indeed mergeable or can be made mergeable after appropriate modifications. Specifically, we show that for ϵ-approximate heavy hitters, there is a deterministic mergeable summary of size $\textit{O}(1/ϵ);$ for ϵ-approximate quantiles, there is a deterministic summary of size $\textit{O}((1/ϵ)$ log(ϵ $\textit{n}))$ that has a restricted form of mergeability, and a randomized one of size $\textit{O}((1/ϵ)$ $log^{3/2}(1/ϵ))$ with full mergeability. We also extend our results to geometric summaries such as ϵ-approximations which permit approximate multidimensional range counting queries. While most of the results in this article are theoretical in nature, some of the algorithms are actually very simple and even perform better than the previously best known algorithms, which we demonstrate through experiments in a simulated sensor network. We also achieve two results of independent interest: (1) we provide the best known randomized streaming bound for ϵ-approximate quantiles that depends only on ϵ, of size $\textit{O}((1/ϵ)$ $log^{3/2}(1/ϵ)),$ and (2) we demonstrate that the MG and the SpaceSaving summaries for heavy hitters are isomorphic.
Starting Page 1
Ending Page 28
Page Count 28
File Format PDF
ISSN 03625915
e-ISSN 15574644
DOI 10.1145/2500128
Volume Number 38
Issue Number 4
Journal ACM Transactions on Database Systems (TODS)
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2013-12-04
Publisher Place New York
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Data summarization Heavy hitters Quantiles
Content Type Text
Resource Type Article
Subject Information Systems
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