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Erschienen in:
2009 | OriginalPaper | Buchkapitel
A Note on Estimating Hybrid Frequency Moment of Data Streams
verfasst von : Sumit Ganguly
Erschienen in: Algorithmic Aspects in Information and Management
Verlag: Springer Berlin Heidelberg
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We consider the problem of estimating the hybrid frequency moment of matrix data that is updated point-wise in arbitrary order by a data stream. In this model, data is viewed to be organized in the form of a matrix (
A
i
,
j
)
1 ≤
i
,
j
, ≤
n
. The entries
A
i
,
j
are updated coordinate-wise (both increments and decrements are allowed), in arbitrary order and possibly multiple times. The hybrid frequency moment
F
p
,
q
(
A
) is defined as
$\sum_{j=1}^n\left( \sum_{i=1}^n \lvert{A_{i,j}}\rvert^p\right)^q$
and is a generalization of the frequency moment of one-dimensional data streams.
Prior work [10] presented a nearly space-optimal algorithm for estimating
F
p
,
q
for
p
∈ [0,2] and
q
∈ [0,1]. Here, we complement that work by presenting a nearly space-optimal algorithm for estimating
F
p
,
q
for
p
∈ [0,1] and
q
∈ [0,2].