Effective computations on sliding windows

SIAM Journal on Computing

Volumn 39, Issue 6, 2010, Pages 2113-2131

  Braverman, Vladimir ^a   Ostrovsky, Rafail ^a  

^a University of California   (United States)

Author keywords

Data streams; Randomized algorithms; Sliding windows; Smooth histograms

Indexed keywords

APPROXIMATION ERRORS; DATA STREAM; GEOMETRIC MEAN; HISTOGRAM METHOD; NON-TRIVIAL TASKS; RANDOMIZED ALGORITHMS; SLIDING WINDOW; STREAMING MODEL;

DATA COMMUNICATION SYSTEMS; ELECTRIC CONVERTERS; GRAPHIC METHODS; STATISTICAL METHODS;

APPROXIMATION ALGORITHMS;

EID: 77952265088     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/090749281     Document Type: Article

References (34)

1. P. K. AGARWAL, S. HAR-PELED, AND K. R. VARADARAJAN, Geometric Approximation via Coresets, in Combinatorial and Computational Geometry, Math. Sci. Res. Inst. Publ. 52, Cambridge University Press, Cambridge, UK, 2005, pp. 1-30.
2. C. C. AGGARWAL, Data Streams: Models and Algorithms (Advances in Database Systems), Springer-Verlag, New York, 2006.
3. N. ALON, Y. MATIAS, AND M. SZEGEDY, The space complexity of approximating the frequency moments, J. Comput. System Sci., 58 (1999), pp. 137-147.
4. A. ARASU AND G. S. MANKU, Approximate counts and quantiles over sliding windows,in Proceedings of the 23rd ACM SIGMOD-SIGART Symposium on Principles of Database Systems, Paris, 2004, pp. 286-296.
5. B. BABCOCK, M. DATAR, AND R. MOTWANI, Sampling from a moving window over streaming data, in Proceedings of the 13th ACM-SIAM Symposium on Discrete Algorithms, San Francisco, 2002, pp. 633-634.
6. B. BABCOCK, M. DATAR, R. MOTWANI, AND L. O'CALLAGHAN, Maintaining variance and kmedians over data stream windows, in Proceedings of the 22nd ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, San Diego, 2003, pp. 234-243.
7. Z. BAR-YOSSEF, T. S. JAYRAM, R. KUMAR, AND D. SIVAKUMAR, An information statistics approach to data stream and communication complexity, J. Comput. System Sci., 68 (2004), pp. 702-732.
8. L. BHUVANAGIRI, S. GANGULY, D. KESH, AND C. SAHA, Simpler algorithm for estimating frequency moments of data streams, in Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms, Miami, 2006, pp. 708-713.
9. V. BRAVERMAN, R. OSTROVSKY, AND C. ZANIOLO, Optimal sampling from sliding windows,in Proceedings of the 28th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, Providence, 2009, pp. 147-156.
10. A. CHAKRABARTI, S. KHOT, AND X. SUN, Near-optimal lower bounds on the multi-party communication complexity of set disjointness, in Proceedings of the 18th IEEE Conference on Computational Complexity, Aarhus, Denmark, 2003, pp. 107-117.
11. T. M. CHAN AND B. S. SADJAD, Geometric optimization problems over sliding windows,Internat. J. Comput. Geom. Appl., 16 (2006), pp. 145-158.
12. E. CHEN, L. YANG, AND H. YUAN, Longest increasing subsequences in windows based on canonical antichain partition, Theoret. Comput. Sci., 378 (2007), pp. 223-236.
13. Y. CHI, H. WANG, P. S. YU, AND R. R. MUNTZ, Moment: Maintaining closed frequent itemsets over a stream sliding window, in Proceedings of the Fourth IEEE International Conference on Data Mining, Brighton, UK, 2004, pp. 59-66.
14. I. COOPER, Arithmetic versus geometric mean estimators: Setting discount rates for capital budgeting, European Financial Management, 2 (1996), pp. 157-167.
15. D. COPPERSMITH AND R. KUMAR, An improved data stream algorithm for frequency moments, in Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms, New Orleans, 2004, pp. 151-156.
16. G. CORMODE, S. TIRTHAPURA, AND B. XU, Time-decaying sketches for sensor data aggregation, in Proceedings of the 26th ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems, Beijing, 2007, pp. 215-224.
17. M. DATAR, A. GIONIS, P. INDYK, AND R. MOTWANI, Maintaining stream statistics over sliding windows, SIAM J. Comput., 31 (2002), pp. 1794-1813.
18. M. DATAR AND S. MUTHUKRISHNAN, Estimating rarity and similarity over data stream windows, in Proceedings of the 10th European Symposium on Algorithms, Rome, 2002, pp. 323-334.
19. J. FEIGENBAUM, S. KANNAN, AND J. ZHANG, Computing diameter in the streaming and sliding- window models, Algorithmica, 41 (2004), pp. 25-41.
20. S. GANGULY, Estimating frequency moments of data streams using random linear combinations, in Proceedings of the APPROX-RANDOM 2004, Cambridge, MA, 2004, pp. 369-380.
21. P. B. GIBBONS AND S. TIRTHAPURA, Distributed streams algorithms for sliding windows, in Proceedings of the 14th ACM Symposium on Parallel Algorithms and Architectures, Winnipeg, Manitoba, Canada, 2002, pp. 63-72.
22. P. GOPALAN, T. S. JAYRAM, R. KRAUTHGAMER, AND R. KUMAR, Estimating the sortedness of a data stream, in Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms 2007, New Orleans, pp. 318-327.
23. S. GUHA, D. GUNOPULOS, AND N. KOUDAS, Correlating synchronous and asynchronous data streams, in Proceedings of the Ninth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, Washington, DC, 2003, pp. 529-534.
24. D. GUSFIELD, Algorithms on Strings, Trees, and Sequences: Computer Science and Computational Biology, Cambridge University Press, Cambridge, UK, 1997.
25. P. INDYK, Stable distributions, pseudorandom generators, embeddings, and data stream computation, J. ACM, 53 (2006), pp. 307-323.
26. P. INDYK AND D. WOODRUFF, Optimal approximations of the frequency moments of data streams, in Proceedings of the 37th ACM Symposium on Theory of Computing, Baltimore, 2005, pp. 202-208.
27. D. M. KANE, J. NELSON, AND D. P. WOODRUFF, Revisiting Norm Estimation in Data Streams, http://www.mit.edu/~minilek/papers/norms.pdf (2008).
28. L. K. LEE AND H. F. TING, Maintaining significant stream statistics over sliding windows, in Proceedings of the 17th ACM-SIAM Symposium on Discrete Algorithms, Miami, 2006, pp. 724-732.
29. L. K. LEE AND H. F. TING, A simpler and more eficient deterministic scheme for finding frequent items over sliding windows, in Proceedings of the 25th ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems, Chicago, 2006, pp. 290-297.
30. D. LIBEN-NOWELL, E. VEE, AND A. ZHU, Finding longest increasing and common subsequences in streaming data, J. Comb. Optim., 11 (2003), p. 2006.
31. S. MUTHUKRISHNAN, Data streams: Algorithms and applications, Found. Trends Theor. Comput. Sci., 1 (2005), pp. 117-236.
32. P. A. PEVZNER, Computational Molecular Biology, MIT Press, Cambridge, MA, 2000.
33. X. SUN AND D. P. WOODRUFF, The communication and streaming complexity of computing the longest common and increasing subsequences, in Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms, New Orleans, 2007, pp. 336-345.
34. S. TIRTHAPURA, B. XU, AND C. BUSCH, Sketching asynchronous streams over a sliding window, in Proceedings of the 25th ACM Symposium on Principles of Distributed Computing, Denver, 2006, pp. 82-91.