Abstract
There is much focus in the algorithms and database communities on designing tools to manage and mine data streams. Typically, data streams consist of multiple signals. Formally, a stream of multiple signals is (i, ai,j) where i's correspond to the domain, j's index the different signals and a i,j ≥ 0 give the value of the jth signal at point i. We study the problem of finding norms that are cumulative of the multiple signals in the data stream. For example, consider the max-dominance norm, defined as ∑i maxj{ai,j}. It may be thought as estimating the norm of the "upper envelope" of the multiple signals, or alternatively, as estimating the norm of the "marginal" distribution of tabular data streams. It is used in applications to estimate the "worst case influence" of multiple processes, for example in IP traffic analysis, electrical grid monitoring and financial domain. In addition, it is a natural measure, generalizing the union of data streams or counting distinct elements in data streams. We present the first known data stream algorithms for estimating max-dominance of multiple signals. In particular, we use workspace and time-per-item that are both sublinear (in fact, poly-logarithmic) in the input size. In contrast other notions of dominance on streams a, b - min-dominance (∑i minj{a i,j}), countdominance (|{i|ai > bi}|) or relative-dominance (∑i ai/ max{1, bi}) - are all impossible to estimate accurately with sublinear space.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 148-160 |
| Number of pages | 13 |
| Journal | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Volume | 2832 |
| State | Published - Dec 1 2003 |
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ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
Cite this
Estimating dominance norms of multiple data streams. / Cormode, Graham; Muthukrishnan, Shanmugavelayutham.
In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 2832, 01.12.2003, p. 148-160.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Estimating dominance norms of multiple data streams
AU - Cormode, Graham
AU - Muthukrishnan, Shanmugavelayutham
PY - 2003/12/1
Y1 - 2003/12/1
N2 - There is much focus in the algorithms and database communities on designing tools to manage and mine data streams. Typically, data streams consist of multiple signals. Formally, a stream of multiple signals is (i, ai,j) where i's correspond to the domain, j's index the different signals and a i,j ≥ 0 give the value of the jth signal at point i. We study the problem of finding norms that are cumulative of the multiple signals in the data stream. For example, consider the max-dominance norm, defined as ∑i maxj{ai,j}. It may be thought as estimating the norm of the "upper envelope" of the multiple signals, or alternatively, as estimating the norm of the "marginal" distribution of tabular data streams. It is used in applications to estimate the "worst case influence" of multiple processes, for example in IP traffic analysis, electrical grid monitoring and financial domain. In addition, it is a natural measure, generalizing the union of data streams or counting distinct elements in data streams. We present the first known data stream algorithms for estimating max-dominance of multiple signals. In particular, we use workspace and time-per-item that are both sublinear (in fact, poly-logarithmic) in the input size. In contrast other notions of dominance on streams a, b - min-dominance (∑i minj{a i,j}), countdominance (|{i|ai > bi}|) or relative-dominance (∑i ai/ max{1, bi}) - are all impossible to estimate accurately with sublinear space.
AB - There is much focus in the algorithms and database communities on designing tools to manage and mine data streams. Typically, data streams consist of multiple signals. Formally, a stream of multiple signals is (i, ai,j) where i's correspond to the domain, j's index the different signals and a i,j ≥ 0 give the value of the jth signal at point i. We study the problem of finding norms that are cumulative of the multiple signals in the data stream. For example, consider the max-dominance norm, defined as ∑i maxj{ai,j}. It may be thought as estimating the norm of the "upper envelope" of the multiple signals, or alternatively, as estimating the norm of the "marginal" distribution of tabular data streams. It is used in applications to estimate the "worst case influence" of multiple processes, for example in IP traffic analysis, electrical grid monitoring and financial domain. In addition, it is a natural measure, generalizing the union of data streams or counting distinct elements in data streams. We present the first known data stream algorithms for estimating max-dominance of multiple signals. In particular, we use workspace and time-per-item that are both sublinear (in fact, poly-logarithmic) in the input size. In contrast other notions of dominance on streams a, b - min-dominance (∑i minj{a i,j}), countdominance (|{i|ai > bi}|) or relative-dominance (∑i ai/ max{1, bi}) - are all impossible to estimate accurately with sublinear space.
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M3 - Article
AN - SCOPUS:0142245899
VL - 2832
SP - 148
EP - 160
JO - Lecture Notes in Computer Science
JF - Lecture Notes in Computer Science
SN - 0302-9743
ER -