The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
Maintaining Stream Statistics over Sliding Windows
Abstract
We consider the problem of maintaining aggregates and statistics over data streams, with respect to the last N data elements seen so far. We refer to this model as the sliding window model. We consider the following basic problem: Given a stream of bits, maintain a count of the number of 1's in the last N elements seen from the stream. We show that, using $O(\frac{1}{\epsilon} \log^2 N)$ bits of memory, we can estimate the number of 1's to within a factor of $1 + \epsilon$. We also give a matching lower bound of $\Omega(\frac{1}{\epsilon}\log^2 N)$ memory bits for any deterministic or randomized algorithms. We extend our scheme to maintain the sum of the last N positive integers and provide matching upper and lower bounds for this more general problem as well. We also show how to efficiently compute the L p norms ($p \in [1,2]$) of vectors in the sliding window model using our techniques. Using our algorithm, one can adapt many other techniques to work for the sliding window model with a multiplicative overhead of $O(\frac{1}{\epsilon}\log N)$ in memory and a $1 +\epsilon$ factor loss in accuracy. These include maintaining approximate histograms, hash tables, and statistics or aggregates such as sum and averages.
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Motwani, R., & Raghavan, P. (1995) · Cambridge University Press eBooks · doi:10.1017/cbo9780511814075 · Cited by 5,123
Self-citationThe space complexity of approximating the frequency moments
Alon, N., Matias, Y., & Szegedy, M. (1996) · Proceedings of the twenty-eighth annual ACM symposium on Theory of computing - STOC '96 · doi:10.1145/237814.237823 · Cited by 822
Guha, S., Mishra, N., Motwani, R., & O'Callaghan, L. (2002) · Proceedings 41st Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2000.892124 · Cited by 623
Self-citationHenzinger, M., Raghavan, P., & Rajagopalan, S. (1999) · DIMACS Series in Discrete Mathematics and Theoretical Computer Science · doi:10.1090/dimacs/050/05 · Cited by 418
Surfing Wavelets on Streams: One-Pass Summaries for Approximate Aggregate Queries
Gilbert, A. C., Kotidis, Y., Muthukrishnan, S., & Strauss, M. J. (2001) · Cited by 376
Computing Iceberg Queries Efficiently
Fang, M., Shivakumar, N., García-Molina, H., Motwani, R., & Ullman, J. D. (1998) · Cited by 340
Self-citationStable distributions, pseudorandom generators, embeddings and data stream computation
Indyk, P. (2002) · Proceedings 41st Annual Symposium on Foundations of Computer Science · doi:10.1109/sfcs.2000.892082 · Cited by 238
Self-citationHancock: a language for extracting signatures from data streams
Cortes, C., Fisher, K., Pregibon, D., & Rogers, A. (2000) · Proceedings of the sixth ACM SIGKDD international conference on Knowledge discovery and data mining · doi:10.1145/347090.347094 · Cited by 179
Nolan, J. P. (2002) · Cited by 178
An Approximate L p-Difference Algorithm for Massive Data Streams: Extended Abstract
Fong, J. H., & Strauss, M. J. (2000) · Lecture Notes in Computer Science · doi:10.1007/3-540-46541-3_16 · Cited by 163
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Gama, J., Žliobaitė, I., Bifet, A., Pechenizkiy, M., & Bouchachia, A. (2014) · ACM Computing Surveys · doi:10.1145/2523813 · Cited by 3,735
Gong, W., Qi, L., & Xu, Y. (2018) · Wireless Communications and Mobile Computing · doi:10.1155/2018/3075849 · Cited by 166
Temporal abstraction in intelligent clinical data analysis: A survey
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Metadata
- Authors
- Datar, M., Gionis, A., Indyk, P., & Motwani, R.
- Venue
- SIAM Journal on Computing
- Published
- 2002-01
- Volume
- 31
- Issue
- 6
- Pages
- 1794-1813
- ISSN
- 0097-5397 (ISSN-L)
- 1095-7111
- OpenAlex
- W2004110412
- Cited by
- 835
- References
- 11
- FWCI
- 55.89
- Type
- journal article
- Language
- en
- Open access
- closed
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