On computing correlated aggregates over continual data streams

ABSTRACT

In many applications from telephone fraud detection to network management, data arrives in a stream, and there is a need to maintain a variety of statistical summary information about a large number of customers in an online fashion. At present, such applications maintain basic aggregates such as running extrema values (MIN, MAX), averages, standard deviations, etc., that can be computed over data streams with limited space in a straightforward way. However, many applications require knowledge of more complex aggregates relating different attributes, so-called correlated aggregates. As an example, one might be interested in computing the percentage of international phone calls that are longer than the average duration of a domestic phone call. Exact computation of this aggregate requires multiple passes over the data stream, which is infeasible.

We propose single-pass techniques for approximate computation of correlated aggregates over both landmark and sliding window views of a data stream of tuples, using a very limited amount of space. We consider both the case where the independent aggregate (average duration in the example above) is an extrema value and the case where it is an average value, with any standard aggregate as the dependent aggregate; these can be used as building blocks for more sophisticated aggregates. We present an extensive experimental study based on some real and a wide variety of synthetic data sets to demonstrate the accuracy of our techniques. We show that this effectiveness is explained by the fact that our techniques exploit monotonicity and convergence properties of aggregates over data streams.

REFERENCES

• 1: Noga Alon , Yossi Matias , Mario Szegedy, The space complexity of approximating the frequency moments, Journal of Computer and System Sciences, v.58 n.1, p.137-147, Feb. 1999 [doi>10.1006/jcss.1997.1545]
• 2: Khaled Alsabti , Sanjay Ranka , Vineet Singh, A One-Pass Algorithm for Accurately Estimating Quantiles for Disk-Resident Data, Proceedings of the 23rd International Conference on Very Large Data Bases, p.346-355, August 25-29, 1997
• 3: Ron Avnur , Joseph M. Hellerstein, Eddies: continuously adaptive query processing, Proceedings of the 2000 ACM SIGMOD international conference on Management of data, p.261-272, May 15-18, 2000, Dallas, Texas, United States
• 4: Ad Hoc OLAP: Expression and Evaluation, Proceedings of the 15th International Conference on Data Engineering, p.250, March 23-26, 1999
• 5: Damianos Chatziantoniou , Michael O. Akinde , Theodore Johnson , Samuel Kim, The MD-join: An Operator for Complex OLAP, Proceedings of the 17th International Conference on Data Engineering, p.524-533, April 02-06, 2001
• 6: Damianos Chatziantoniou , Kenneth A. Ross, Querying Multiple Features of Groups in Relational Databases, Proceedings of the 22th International Conference on Very Large Data Bases, p.295-306, September 03-06, 1996
• 7: A. Delis, C. Faloutsos, and S. Ghandeharizadeh, editors. SIGMOD 1999, Proceedings ACM SIGMOD International Conference on Management of Data, June 1-3, 1999, Philadephia, PJjennsylvania, USA. ACM Press, 1999.
• 8: Pedro Domingos , Geoff Hulten, Mining high-speed data streams, Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining, p.71-80, August 20-23, 2000, Boston, Massachusetts, United States [doi>10.1145/347090.347107]
• 9: J. Feigenbaum , S. Kannan , M. Strauss , M. Viswanathan, An Approximate L1-Difference Algorithm for Massive Data Streams, Proceedings of the 40th Annual Symposium on Foundations of Computer Science, p.501, October 17-18, 1999
• 10: J. Feigenbaum , S. Kannan , M. Strauss , M. Viswanathan, Testing and spot-checking of data streams (extended abstract), Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms, p.165-174, January 09-11, 2000, San Francisco, California, United States
• 11: A. Feldmann , A. C. Gilbert , W. Willinger, Data networks as cascades: investigating the multifractal nature of Internet WAN traffic, Proceedings of the ACM SIGCOMM '98 conference on Applications, technologies, architectures, and protocols for computer communication, p.42-55, August 31-September 04, 1998, Vancouver, British Columbia, Canada
• 12: Jessica H. Fong , Martin Strauss, An Approximate Lp-Difference Algorithm for Massive Data Streams, Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science, p.193-204, February 01, 2000
• 13: Johannes Gehrke , Venkatesh Ganti , Raghu Ramakrishnan , Wei-Yin Loh, BOAT—optimistic decision tree construction, Proceedings of the 1999 ACM SIGMOD international conference on Management of data, p.169-180, May 31-June 03, 1999, Philadelphia, Pennsylvania, United States
• 14: Phillip B. Gibbons , Yossi Matias , Viswanath Poosala, Fast Incremental Maintenance of Approximate Histograms, Proceedings of the 23rd International Conference on Very Large Data Bases, p.466-475, August 25-29, 1997
• 15: Phillip B. Gibbons , Yossi Matias, Synopsis data structures for massive data sets, Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms, p.909-910, January 17-19, 1999, Baltimore, Maryland, United States
• 16: S. Guha , N. Mishra , R. Motwani , L. O'Callaghan, Clustering data streams, Proceedings of the 41st Annual Symposium on Foundations of Computer Science, p.359, November 12-14, 2000
• 17: Peter J. Haas , Joseph M. Hellerstein, Ripple joins for online aggregation, Proceedings of the 1999 ACM SIGMOD international conference on Management of data, p.287-298, May 31-June 03, 1999, Philadelphia, Pennsylvania, United States
• 18: Joseph M. Hellerstein , Peter J. Haas , Helen J. Wang, Online aggregation, Proceedings of the 1997 ACM SIGMOD international conference on Management of data, p.171-182, May 11-15, 1997, Tucson, Arizona, United States
• 19: M.R. Henzinger, P. Raghavan, and S. Rajagopalan. Computing on data streams. Technical Report 1998-011, Digital Equipment Corporation, Systems Research Center, May, 1998.
• 20: Gurmeet Singh Manku , Sridhar Rajagopalan , Bruce G. Lindsay, Approximate medians and other quantiles in one pass and with limited memory, Proceedings of the 1998 ACM SIGMOD international conference on Management of data, p.426-435, June 01-04, 1998, Seattle, Washington, United States
• 21: Gurmeet Singh Manku , Sridhar Rajagopalan , Bruce G. Lindsay, Random sampling techniques for space efficient online computation of order statistics of large datasets, Proceedings of the 1999 ACM SIGMOD international conference on Management of data, p.251-262, May 31-June 03, 1999, Philadelphia, Pennsylvania, United States
• 22: Chris Olston , Jennifer Widom, Offering a Precision-Performance Tradeoff for Aggregation Queries over Replicated Data, Proceedings of the 26th International Conference on Very Large Data Bases, p.144-155, September 10-14, 2000
• 23: Vijayshankar Raman , Bhaskaran Raman , Joseph M. Hellerstein, Online Dynamic Reordering for Interactive Data Processing, Proceedings of the 25th International Conference on Very Large Data Bases, p.709-720, September 07-10, 1999

INDEX TERMS

Primary Classification:
  H. Information Systems
  H.2 DATABASE MANAGEMENT

General Terms:
Algorithms, Design, Experimentation, Management, Measurement, Performance, Reliability, Security, Theory