DMCA
Maintaining Stream Statistics over Sliding Windows (Extended Abstract) (2002)
Cached
Download Links
- [www.stanford.edu]
- [www-cs-students.stanford.edu]
- [www-cs.stanford.edu]
- [www.dei.unipd.it]
- DBLP
Other Repositories/Bibliography
| Citations: | 269 - 9 self |
BibTeX
@MISC{Datar02maintainingstream,
author = {Mayur Datar and Aristides Gionis and Piotr Indyk and Rajeev Motwani},
title = {Maintaining Stream Statistics over Sliding Windows (Extended Abstract)},
year = {2002}
}
Share
 |
 |
 |
 |
||
OpenURL
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( 1 ffl log 2 N) bits of memory, we can estimate the number of 1's to within a factor of 1 + ffl. We also give a matching lower bound of \Omega\Gamma 1 ffl 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. We provide matching upper and lower bounds for this more general problem as well. We apply our techniques to obtain efficient algorithms for the Lp norms (for p 2 [1; 2]) of vectors under the sliding window model. Using the algorithm for the basic counting problem, one can adapt many other techniques to work for the sliding window model, with a multiplicative overhead of O( 1 ffl log N) in memory and a 1 + ffl factor loss in accuracy. These include maintaining approximate histograms, hash tables, and statistics or aggregates such as sum and averages.
Keyphrases
sliding window model extended abstract stream statistic ffl log basic counting problem last element ffl factor loss basic problem last data element efficient algorithm approximate histogram memory bit multiplicative overhead last positive integer data stream hash table lp norm omega gamma general problem many technique
