skip to main content
10.1145/1993744.1993763acmconferencesArticle/Chapter ViewAbstractPublication PagesmetricsConference Proceedingsconference-collections
research-article

Structure-aware sampling on data streams

Published: 07 June 2011 Publication History

Abstract

The massive data streams observed in network monitoring, data processing and scientific studies are typically too large to store. For many applications over such data, we must obtain compact summaries of the stream. These summaries should allow accurate answering of post hoc queries with estimates which approximate the true answers over the original stream. The data often has an underlying structure which makes certain subset queries, in particular range queries, more relevant than arbitrary subsets. Applications such as access control, change detection, and heavy hitters typically involve subsets that are ranges or unions thereof.
Random sampling is a natural summarization tool, being easy to implement and flexible to use. Known sampling methods are good for arbitrary queries but fail to optimize for the common case of range queries. Meanwhile, specialized summarization algorithms have been proposed for rangesum queries and related problems. These can outperform sampling giving fixed space resources, but lack its flexibility and simplicity. Particularly, their accuracy degrades when queries span multiple ranges.
We define new stream sampling algorithms with a smooth and tunable trade-off between accuracy on range-sum queries and arbitrary subset-sum queries. The technical key is to relax requirements on the variance over all subsets to enable better performance on the ranges of interest. This boosts the accuracy on range queries while retaining the prime benefits of sampling, in particular flexibility and accuracy, with tail bounds guarantees. Our experimental study indicates that structure-aware summaries can drastically improve range-sum accuracy with respect to state-of-the-art stream sampling algorithms and outperform deterministic methods on range-sum queries and hierarchical heavy hitter queries.

References

[1]
C. Buragohain and S. Suri. Quantiles on streams. In Encyclopedia of Database Systems. Springer, 2009.
[2]
M. T. Chao. A general purpose unequal probability sampling plan. Biometrika, 69(3):653--656, 1982.
[3]
H. Chernoff. A measure of the asymptotic efficiency for test of a hypothesis based on the sum of observations. Annals of Math. Statistics, 23:493--509, 1952.
[4]
E. Cohen, G. Cormode and N. Duffield. Structure-aware sampling: Flexible and accurate summarization. arXiv:1102.5146, 2011.
[5]
E. Cohen, N. Duffield, H. Kaplan, C. Lund, and M. Thorup. Stream sampling for variance-optimal estimation of subset sums. In ACM-SIAM SODA, 2009.
[6]
E. Cohen, N. Duffield, H. Kaplan, C. Lund, and M. Thorup. Composable, Scalable, and Accurate Weight Summarization of Unaggregated Data Sets In VLDB, 2009.
[7]
E. Cohen, N. Duffield, C. Lund, M. Thorup, and H. Kaplan. Variance optimal sampling based estimation of subset sums. Tech. report arXiv:0803.0473v1 {cs.DS}, 2008.
[8]
G. Cormode and M. Hadjieleftheriou. Finding frequent items in data streams. In VLDB, 2008.
[9]
G. Cormode, F. Korn, S. Muthukrishnan, and D. Srivastava. Space- and time-efficient deterministic algorithms for biased quantiles over data streams. In ACM PODS, 2006.
[10]
G. Cormode, F. Korn, S. Muthukrishnan, and D. Srivastava. Finding hierarchical heavy hitters in streaming data. ACM Trans. Knowl. Discov. Data, 1(4):1--48, 2008.
[11]
R. Gandhi, S. Khuller, S. Parthasarathy, and A. Srinivasan. Dependent rounding and its applications to approximation algorithms. J. Assoc. Comput. Mach., 53(3):324--360, 2006.
[12]
J. Hájek. Sampling from a finite population. Marcel Dekker, 1981.
[13]
D. G. Horvitz and D. J. Thompson. A generalization of sampling without replacement from a finite universe. J. Amer. Stat. Assoc., 47(260):663--685, 1952.
[14]
A. Panconesi and A. Srinivasan. Randomized distributed edge coloring via an extension of the Chernoff-Hoeffding bounds. SIAM J. Comput., 26(2):350--368, 1997.
[15]
N. Shrivastava, C. Buragohain, D. Agrawal, and S. Suri. Medians and beyond: new aggregation techniques for sensor networks. In ACM SenSys, 2004.
[16]
A. Srinivasan. Distributions on level-sets with applications to approximation algorithms. In IEEE FOCS. 2001.
[17]
M. Szegedy and M. Thorup. On the variance of subset sum estimation. In Proc. ESA, 2007.
[18]
Y. Tillé. Sampling Algorithms, Springer, 2006.
[19]
J. Vitter. Random sampling with a reservoir. ACM Trans. Math. Softw., 11(1):37--57, 1985.
[20]
Y. Zhang, S. Singh, S. Sen, N. Duffield, and C. Lund. Online identification of hierarchical heavy hitters. In SIGMETRICS, 2004.

Cited By

View all
  • (2021)LATEST: Learning-Assisted Selectivity Estimation Over Spatio-Textual Streams2021 IEEE 37th International Conference on Data Engineering (ICDE)10.1109/ICDE51399.2021.00142(1607-1618)Online publication date: Apr-2021
  • (2019)Comparing synopsis techniques for approximate spatial data analysisProceedings of the VLDB Endowment10.14778/3342263.334263512:11(1583-1596)Online publication date: 1-Jul-2019
  • (2019)Continuously Distinct Sampling over Centralized and Distributed High Speed Data StreamsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2018.286545230:2(300-314)Online publication date: 1-Feb-2019
  • Show More Cited By

Index Terms

  1. Structure-aware sampling on data streams

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Conferences
    SIGMETRICS '11: Proceedings of the ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
    June 2011
    376 pages
    ISBN:9781450308144
    DOI:10.1145/1993744
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

    Sponsors

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 07 June 2011

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tags

    1. approximate query processing
    2. data streams
    3. structure-aware sampling
    4. varopt

    Qualifiers

    • Research-article

    Conference

    SIGMETRICS '11
    Sponsor:

    Acceptance Rates

    Overall Acceptance Rate 459 of 2,691 submissions, 17%

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)3
    • Downloads (Last 6 weeks)1
    Reflects downloads up to 07 Mar 2025

    Other Metrics

    Citations

    Cited By

    View all
    • (2021)LATEST: Learning-Assisted Selectivity Estimation Over Spatio-Textual Streams2021 IEEE 37th International Conference on Data Engineering (ICDE)10.1109/ICDE51399.2021.00142(1607-1618)Online publication date: Apr-2021
    • (2019)Comparing synopsis techniques for approximate spatial data analysisProceedings of the VLDB Endowment10.14778/3342263.334263512:11(1583-1596)Online publication date: 1-Jul-2019
    • (2019)Continuously Distinct Sampling over Centralized and Distributed High Speed Data StreamsIEEE Transactions on Parallel and Distributed Systems10.1109/TPDS.2018.286545230:2(300-314)Online publication date: 1-Feb-2019
    • (2019)A survey on quality-assurance approximate stream processing and applicationsFuture Generation Computer Systems10.1016/j.future.2019.07.047Online publication date: Jul-2019
    • (2019)Selectivity Estimation on Set Containment SearchData Science and Engineering10.1007/s41019-019-00104-14:3(254-268)Online publication date: 23-Sep-2019
    • (2019)Selectivity Estimation on Set Containment SearchDatabase Systems for Advanced Applications10.1007/978-3-030-18576-3_20(330-349)Online publication date: 24-Apr-2019
    • (2019)Accelerating Real-Time Tracking Applications over Big Data Stream with Constrained SpaceDatabase Systems for Advanced Applications10.1007/978-3-030-18576-3_1(3-18)Online publication date: 22-Apr-2019
    • (2016)From Business Intelligence to semantic data stream managementFuture Generation Computer Systems10.1016/j.future.2015.11.01563:C(100-107)Online publication date: 1-Oct-2016
    • (2014)Selectivity estimation on streaming spatio-textual data using local correlationsProceedings of the VLDB Endowment10.14778/2735471.27354728:2(101-112)Online publication date: 1-Oct-2014
    • (2014)Adaptive stratified reservoir sampling over heterogeneous data streamsInformation Systems10.1016/j.is.2012.03.00539(199-216)Online publication date: 1-Jan-2014
    • Show More Cited By

    View Options

    Login options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Figures

    Tables

    Media

    Share

    Share

    Share this Publication link

    Share on social media