Abstract.
We present a randomized procedure named Hierarchical Sampling from Sketches (HSS) that can be used for estimating a class of functions over the frequency vector f of update streams of the form (S) = Pn i=1 (|fi|).We illustrate this by applying the HSS technique to design nearly space-optimal algorithms for estimating the pth moment of the frequency vector, for real p _ 2 and for estimating the entropy of a data stream. 3
1 Introduction
A variety of applications in diverse areas, such as, networking, database sys ....etc

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Abstract
The problem of estimating the kth frequency moment Fk over a data stream by looking at the items exactly once as they arrive was posed in . A succession of algorithms have been proposed for this problem . Recently, Indyk and Woodru® have presented the ¯rst algorithm for estimating Fk, for k > 2, using space ~O (n1¡2=k), matching the space lower bound (up to poly-logarithmic factors) for this problem (n is the number of distinct items occurring in the stream.) In this paper, we pre ....etc

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Abstract—Despite its promise, RFID technology presents numerous challenges, including incomplete data, lack of location and containment information, and very high volumes. In this work, we present a novel data inference and compression substrate over RFID streams to address these challenges. Our substrate employs a time-varying graph model to efficiently capture possible object locations and interobject relationships such as containment from raw RFID streams. It then employs a probabilistic algorithm to estimate the most likely location and c ....etc

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Abstract.
We present an algorithm for estimating entropy of data streams consisting of insertion and deletion operations using ~O(1) space.
1 1 Introduction
Recently, there has been an emergence of monitoring applications in diverse areas, including, network traf_c monitoring, network topology monitoring, sensor networks, _nancial market monitoring, web-log monitoring, etc.. In these applications, data is generated rapidly and continuously, and must be analyzed very ef_ciently, in realtime, to identify large trends, anomalies ....etc

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Abstract.
Space-economical estimation of the pth frequency moments, defined as Fp = Pn i=1|fi|p, for p > 0, are of interest in estimating all-pairs distances in a large data matrix , machine learning, and in data stream computation. Random sketches formed by the inner product of the frequency vector f1, . . . , fn with a suitably chosen random vector were pioneered by Alon, Matias and Szegedy , and have since played a central role in estimating Fp and for data stream computations in general. The concept of p-stable sketches for ....etc

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presented by:
Chedy Ra¨ıssi,Pascal Poncelet,Maguelonne Teisseire

ABSTRACT
Many recent real-world applications, such as network traf-_c monitoring, intrusion detection systems, sensor networkdata analysis, click stream mining and dynamic tracing of_nancial transactions, call for studying a new kind of data.Called stream data, this model is, in fact, a continuous, potentiallyin_nite ow of information as opposed to _nite,statically stored data sets extensively studied by researchersof the data mining community. An important appl ....etc

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Abstract.
The problem of estimating the kth frequency moment Fk, for any
non-negative integral value of k, over a data stream by looking at the items exactly
once as they arrive, was considered in a seminal paper by Alon, Matias and
Szegedy . They present a sampling based algorithm to estimate Fk where,
k  2, using space ˜O(n1−1/k)). Coppersmith and Kumar and , using
different methods, present algorithms for estimating Fk with space complexity
˜O
(n1−1/(k−1)). In this paper, we present an algorithm for es ....etc

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Abstract.
We consider a basic problem in the general data streaming model, namely, to estimate
a vector f 2 Zn that is arbitrarily updated (i.e., incremented or decremented) coordinatewise.
The estimate ˆ f 2 Zn must satisfy k ˆ f − fk1 _ _kfk1, that is, 8i (| ˆ fi −fi| _ _kfk1). It is
known to have ˜O(_−1) randomized space upper bound , (_−1 log(_n)) space lower bound
and deterministic space upper bound of ˜(_−2) bits.1 We show that any deterministic
algorithm for this problem requires space (_−2(logkfk1)) ....etc

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Abstract.
We consider the problem of estimating hybrid frequency moments of two dimensional data
streams. In this model, data is viewed to be organized in a matrix form (Ai;j)1i;j;n. The entries
Ai;j are updated coordinate-wise, in arbitrary order and possibly multiple times. The updates include
both increments and decrements to the current value of Ai;j . The hybrid frequency moment Fp;q(A)
is dened as
Pn
j=1
....etc

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Abstract.
We present deterministic sub-linear space algorithms for a number of problems over update data streams, including, estimating fre- quencies of items and ranges, ¯nding approximate frequent items and approximate Á-quantiles, estimating inner-products, constructing near- optimal B-bucket histograms and estimating entropy. We also present new lower bound results for several problems over update data streams.
1 Introduction
The data streaming model presents a computational model for a variety of monitoring a ....etc

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