The Frequent Items Problem, under Polynomial Decay, in the Streaming Model

Guy Feigenblat; Ofra Itzhaki; E. Porat

The Frequent Items Problem, under Polynomial Decay, in the Streaming Model

Guy Feigenblat, Ofra Itzhaki, E. Porat

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We consider the problem of estimating the frequency count of data stream elements under polynomial decay functions. In these settings every element arrives in the stream is assigned with a time decreasing weight, using a non increasing polynomial function. Decay functions are used in applications where older data is less significant \ interesting \ reliable than recent data. We propose 3 poly-logarithmic algorithms for the problem. The first one, deterministic, uses O(1ϵ2logN(loglogN+logU))O(1ϵ2log⁡N(log⁡log⁡N+log⁡U)) bits. The second one, probabilistic, uses O(1ϵ2log1ϵδlogN)O(1ϵ2log⁡1ϵδlog⁡N) bits and the third one, deterministic in the stochastic model, uses O(1ϵ2logN)O(1ϵ2log⁡N) bits. In addition we show that using additional additive error can improve, in some cases, the space bounds. This variant of the problem is important and has many applications. To our knowledge it was never studied before.

Original language	American English
Title of host publication	International Symposium on String Processing and Information Retrieval
Editors	Jussi Karlgren, Jorma Tarhio, Heikki Hyyrö
Publisher	Springer Berlin Heidelberg
State	Published - 2009

Bibliographical note

Place of conference:Finland

Cite this

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title = "The Frequent Items Problem, under Polynomial Decay, in the Streaming Model",

abstract = "We consider the problem of estimating the frequency count of data stream elements under polynomial decay functions. In these settings every element arrives in the stream is assigned with a time decreasing weight, using a non increasing polynomial function. Decay functions are used in applications where older data is less significant \ interesting \ reliable than recent data. We propose 3 poly-logarithmic algorithms for the problem. The first one, deterministic, uses O(1ϵ2logN(loglogN+logU))O(1ϵ2log⁡N(log⁡log⁡N+log⁡U)) bits. The second one, probabilistic, uses O(1ϵ2log1ϵδlogN)O(1ϵ2log⁡1ϵδlog⁡N) bits and the third one, deterministic in the stochastic model, uses O(1ϵ2logN)O(1ϵ2log⁡N) bits. In addition we show that using additional additive error can improve, in some cases, the space bounds. This variant of the problem is important and has many applications. To our knowledge it was never studied before.",

author = "Guy Feigenblat and Ofra Itzhaki and E. Porat",

note = "Place of conference:Finland",

year = "2009",

language = "American English",

editor = "Jussi Karlgren and Jorma Tarhio and Heikki Hyyr{\"o}",

booktitle = "International Symposium on String Processing and Information Retrieval",

publisher = "Springer Berlin Heidelberg",

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The Frequent Items Problem, under Polynomial Decay, in the Streaming Model. / Feigenblat, Guy; Itzhaki, Ofra; Porat, E.
International Symposium on String Processing and Information Retrieval. ed. / Jussi Karlgren; Jorma Tarhio; Heikki Hyyrö. Springer Berlin Heidelberg, 2009.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - The Frequent Items Problem, under Polynomial Decay, in the Streaming Model

AU - Feigenblat, Guy

AU - Itzhaki, Ofra

AU - Porat, E.

N1 - Place of conference:Finland

PY - 2009

Y1 - 2009

N2 - We consider the problem of estimating the frequency count of data stream elements under polynomial decay functions. In these settings every element arrives in the stream is assigned with a time decreasing weight, using a non increasing polynomial function. Decay functions are used in applications where older data is less significant \ interesting \ reliable than recent data. We propose 3 poly-logarithmic algorithms for the problem. The first one, deterministic, uses O(1ϵ2logN(loglogN+logU))O(1ϵ2log⁡N(log⁡log⁡N+log⁡U)) bits. The second one, probabilistic, uses O(1ϵ2log1ϵδlogN)O(1ϵ2log⁡1ϵδlog⁡N) bits and the third one, deterministic in the stochastic model, uses O(1ϵ2logN)O(1ϵ2log⁡N) bits. In addition we show that using additional additive error can improve, in some cases, the space bounds. This variant of the problem is important and has many applications. To our knowledge it was never studied before.

AB - We consider the problem of estimating the frequency count of data stream elements under polynomial decay functions. In these settings every element arrives in the stream is assigned with a time decreasing weight, using a non increasing polynomial function. Decay functions are used in applications where older data is less significant \ interesting \ reliable than recent data. We propose 3 poly-logarithmic algorithms for the problem. The first one, deterministic, uses O(1ϵ2logN(loglogN+logU))O(1ϵ2log⁡N(log⁡log⁡N+log⁡U)) bits. The second one, probabilistic, uses O(1ϵ2log1ϵδlogN)O(1ϵ2log⁡1ϵδlog⁡N) bits and the third one, deterministic in the stochastic model, uses O(1ϵ2logN)O(1ϵ2log⁡N) bits. In addition we show that using additional additive error can improve, in some cases, the space bounds. This variant of the problem is important and has many applications. To our knowledge it was never studied before.

UR - https://scholar.google.co.il/scholar?q=The+Frequent+Items+Problem%2C+under+Polynomial+Decay%2C+in+the+Streaming+Model&btnG=&hl=en&as_sdt=0%2C5

M3 - Conference contribution

BT - International Symposium on String Processing and Information Retrieval

A2 - Karlgren, Jussi

A2 - Tarhio, Jorma

A2 - Hyyrö, Heikki

PB - Springer Berlin Heidelberg

ER -

The Frequent Items Problem, under Polynomial Decay, in the Streaming Model

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