An information statistics approach to data stream and communication complexity

Bar-Yossef, Ziv; Jayram, T. S.; Kumar, Ravi; Sivakumar, D.

doi:10.1109/sfcs.2002.1181944

Cited by 249 publications

(536 citation statements)

References 23 publications

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“…This shows that the Hss algorithm described in this section for estimating , is nearly space optimal for = 0 or 1 and ∈ [1,2]. The problem of obtaining lower bounds for estimating , for ∈ (0, 2) and ∈ (0, 2), (with the exception of the above cases) is open.…”

Section: Similarly Ifmentioning

confidence: 94%

“…Thus, ∑ =1 0 , counts the number of distinct sources that send at least one message to . Define the hybrid moment 0,2 ( ) = ∑ =1 ( ∑ =1 0 , ) 2 . In an attack scenario, 0,2 ( ) becomes large compared to its average value.…”

Section: Introductionmentioning

confidence: 99%

“…Woodruff [21] presents an ( −2 ) space lower bound for the problem of estimating , for all ≥ 0, implying that the stable sketches technique is space optimal up to poly-logarithmic factors. A space lower bound of ( 1−2/ ) was shown for the problem of estimating for ≥ 2 in a series of developments [1,2,5]. Cormode and Muthukrishnan [8] present an algorithm for obtaining an -approximation for 0,2 ( ) using space˜ ( √ ).…”

Section: Introductionmentioning

confidence: 99%

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Estimating hybrid frequency moments of data streams

2010

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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 ( , ) 1≤ , ,≤ . The entries , are updated coordinate-wise, in arbitrary order and possibly multiple times. The updates include both increments and decrements to the current value of , . The hybrid frequency moment , ( ) is defined asand is a generalization of the frequency moment of one-dimensional data streams. We present an˜ (1) space 1 algorithm for the problem of estimating , for ∈ [0, 2] and ∈ [0, 1]. We also present a˜ ( 1−1/ ) space algorithm for estimating , for ∈ [0, 2] and ∈ (1, 2].

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Section: Similarly Ifmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Estimating hybrid frequency moments of data streams

2010

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“…This is tight following successively improved lower bounds from [14], via e.g. [196] and [21], to finally [31].…”

Section: Moments Estimationmentioning

confidence: 96%

Data Streams: Algorithms and Applications

Muthukrishnan

2005

FNT in Theoretical Computer Science

779

541

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In the data stream scenario, input arrives very rapidly and there is limited memory to store the input. Algorithms have to work with one or few passes over the data, space less than linear in the input size or time significantly less than the input size. In the past few years, a new theory has emerged for reasoning about algorithms that work within these constraints on space, time, and number of passes. Some of the methods rely on metric embeddings, pseudo-random computations, sparse approximation theory and communication complexity. The applications for this scenario include IP network traffic analysis, mining text message streams and processing massive data sets in general. Researchers in Theoretical Computer Science, Databases, IP Networking and Computer Systems are working on the data stream challenges. This article is an overview and survey of data stream algorithmics and is an updated version of [175].

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“…The reader familiar with the techniques of Bar-Yossef, Jayram, Kumar & Sivakumar [BYJKS04], should recall that in the first part of the method a direct-sum for informational complexity of disjointness is proved. In particular, it is shown that with respect to suitable collections of distributions η and ζ for DISJ n,2 and AND 2 respectively, the information cost of DISJ n,2 is at least n times the informational complexity of AND 2 : IC η,δ (DISJ n,2 ) ≥ n · IC ζ,δ (AND 2 ).…”

Section: Difficulties In Proving a Direct-sum Theoremmentioning

confidence: 99%

Hellinger volume and number-on-the-forehead communication complexity

Lee

Leonardos

Saks

et al. 2016

Journal of Computer and System Sciences

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Information-theoretic methods have proven to be a very powerful tool in communication complexity, in particular giving an elegant proof of the linear lower bound for the two-party disjointness function, and tight lower bounds on disjointness in the multi-party number-in-the-hand (NIH) model. In this paper, we study the applicability of information theoretic methods to the multiparty number-on-the-forehead model (NOF), where determining the complexity of disjointness remains an important open problem.There are two basic parts to the NIH disjointness lower bound: a direct sum theorem and a lower bound on the one-bit AND function using a beautiful connection between Hellinger distance and protocols revealed by Bar-Yossef, Jayram, Kumar & Sivakumar [BYJKS04]. Inspired by this connection, we introduce the notion of Hellinger volume. We show that it lower bounds the information cost of multi-party NOF protocols and provide a small toolbox that allows one to manipulate several Hellinger volume terms and lower bound a Hellinger volume when the distributions involved satisfy certain conditions. In doing so, we prove a new upper bound on the difference between the arithmetic mean and the geometric mean in terms of relative entropy. We then apply these new tools to obtain a lower bound on the informational complexity of the AND k function in the NOF setting. Finally, we discuss the difficulties of proving a direct sum theorem for information cost in the NOF model.

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An information statistics approach to data stream and communication complexity

Cited by 249 publications

References 23 publications

Estimating hybrid frequency moments of data streams

Estimating hybrid frequency moments of data streams

Data Streams: Algorithms and Applications

Hellinger volume and number-on-the-forehead communication complexity

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