Volume

Dagstuhl Seminar Proceedings, Volume 8341

Publication Details

  • published at: 2008-11-25
  • Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik

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Document
DOI: 10.4230/DagSemProc.08341.1
08341 Abstracts Collection – Sublinear Algorithms

Authors: Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler

Abstract
From August 17 to August 22, 2008, the Dagstuhl Seminar 08341 ``Sublinear Algorithms'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.
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Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler. 08341 Abstracts Collection – Sublinear Algorithms. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 8341, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{czumaj_et_al:DagSemProc.08341.1,
  author =	{Czumaj, Artur and Muthukrishnan, S. Muthu and Rubinfeld, Ronitt and Sohler, Christian},
  title =	{{08341 Abstracts Collection – Sublinear Algorithms}},
  booktitle =	{Sublinear Algorithms},
  pages =	{1--19},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8341},
  editor =	{Artur Czumaj and S. Muthu Muthukrishnan and Ronitt Rubinfeld and Christian Sohler},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08341.1},
  URN =		{urn:nbn:de:0030-drops-16981},
  doi =		{10.4230/DagSemProc.08341.1},
  annote =	{Keywords: Sublinear algorithms, property testing, data streaming, graph algorithms, approximation algorithms}
}
Document
DOI: 10.4230/DagSemProc.08341.2
08341 Executive Summary – Sublinear Algorithms

Authors: Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler

Abstract
This report summarizes the content and structure of the Dagstuhl seminar `Sublinear Algorithms', which was held from 17.8.2008 to 22.8.2008 in Schloss Dagstuhl, Germany.
Cite as

Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler. 08341 Executive Summary – Sublinear Algorithms. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 8341, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{czumaj_et_al:DagSemProc.08341.2,
  author =	{Czumaj, Artur and Muthukrishnan, S. Muthu and Rubinfeld, Ronitt and Sohler, Christian},
  title =	{{08341 Executive Summary – Sublinear Algorithms}},
  booktitle =	{Sublinear Algorithms},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8341},
  editor =	{Artur Czumaj and S. Muthu Muthukrishnan and Ronitt Rubinfeld and Christian Sohler},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08341.2},
  URN =		{urn:nbn:de:0030-drops-16964},
  doi =		{10.4230/DagSemProc.08341.2},
  annote =	{Keywords: Sublinear algorithms, property testing, data streaming, graph algorithms, approximation algorithms}
}
Document
DOI: 10.4230/DagSemProc.08341.3
Breaking the $\epsilon$-Soundness Bound of the Linearity Test over GF(2)

Authors: Tali Kaufman, Simon Litsyn, and Ning Xie

Abstract
For Boolean functions that are $epsilon$-far from the set of linear functions, we study the lower bound on the rejection probability (denoted by $extsc{rej}(epsilon)$) of the linearity test suggested by Blum, Luby and Rubinfeld. This problem is arguably the most fundamental and extensively studied problem in property testing of Boolean functions. The previously best bounds for $extsc{rej}(epsilon)$ were obtained by Bellare, Coppersmith, H{{a}}stad, Kiwi and Sudan. They used Fourier analysis to show that $ extsc{rej}(epsilon) geq e$ for every $0 leq epsilon leq frac{1}{2}$. They also conjectured that this bound might not be tight for $epsilon$'s which are close to $1/2$. In this paper we show that this indeed is the case. Specifically, we improve the lower bound of $ extsc{rej}(epsilon) geq epsilon$ by an additive constant that depends only on $epsilon$: $extsc{rej}(epsilon) geq epsilon + min {1376epsilon^{3}(1-2epsilon)^{12}, frac{1}{4}epsilon(1-2epsilon)^{4}}$, for every $0 leq epsilon leq frac{1}{2}$. Our analysis is based on a relationship between $extsc{rej}(epsilon)$ and the weight distribution of a coset of the Hadamard code. We use both Fourier analysis and coding theory tools to estimate this weight distribution.
Cite as

Tali Kaufman, Simon Litsyn, and Ning Xie. Breaking the $\epsilon$-Soundness Bound of the Linearity Test over GF(2). In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 8341, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{kaufman_et_al:DagSemProc.08341.3,
  author =	{Kaufman, Tali and Litsyn, Simon and Xie, Ning},
  title =	{{Breaking the \$\backslashepsilon\$-Soundness Bound of the Linearity Test over GF(2)}},
  booktitle =	{Sublinear Algorithms},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8341},
  editor =	{Artur Czumaj and S. Muthu Muthukrishnan and Ronitt Rubinfeld and Christian Sohler},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08341.3},
  URN =		{urn:nbn:de:0030-drops-16971},
  doi =		{10.4230/DagSemProc.08341.3},
  annote =	{Keywords: Linearity test, Fourier analysis, coding theory}
}
Document
DOI: 10.4230/DagSemProc.08341.4
Lower bound for estimating frequency for update data streams

Authors: Sumit Ganguly

Abstract
We consider general update streams, where, the stream is a sequence of updates of the form $(index, i, v)$, where, $i in {1,2 ldots, n}$ and $v in {-1,+1}$, signifying deletion or insertion, respectively of an instance of $i$. The frequency of $i in {1,2,ldots, n}$ is given as the sum of the updates to $i$, that is, $f_i(sigma) = sum_{(index,i,v) in sigma} v $. The $n$-dimensional vector $f(sigma)$ with $i$th coordinate $f_i(sigma)$ is called the frequency vector of the stream $sigma$. We consider the problem of finding an n-dimensional integer vector $hat{f}(sigma)$ that estimates the frequency vector $f(sigma)$ of an input stream $sigma$ in the following sense: orm{hat{f} (sigma)- f(sigma)} le epsilon orm{f(sigma)}_p For $p=1$ and $2$, there are randomized algorithms known with space bound $ ilde{O}(epsilon^{-p})$. A space lower bound of $Omega(epsilon^{-1} log (nepsilon))$ is also known. However, the deterministic space upper bound is $ ilde{O}(epsilon^{-2})$. In this work, we present a deterministic space lower bound of $Omega(n^{2-2/p}epsilon^{-2} log |{sigma}|)$, for $1le p < 2$ and $1/4 le epsilon = Omega(n^{1/2-1/p})$. For $p ge 2$, we show an $Omega(n)$ space lower bound for all $epsilon < 1/4$. The results are obtained using a new characterization of data stream computations, that show that any uniform computation over a data stream may be viewed as an appropriate linear map.
Cite as

Sumit Ganguly. Lower bound for estimating frequency for update data streams. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 8341, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{ganguly:DagSemProc.08341.4,
  author =	{Ganguly, Sumit},
  title =	{{Lower bound for estimating frequency for update data streams}},
  booktitle =	{Sublinear Algorithms},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{8341},
  editor =	{Artur Czumaj and S. Muthu Muthukrishnan and Ronitt Rubinfeld and Christian Sohler},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08341.4},
  URN =		{urn:nbn:de:0030-drops-16959},
  doi =		{10.4230/DagSemProc.08341.4},
  annote =	{Keywords: Data stream, lower bound, frequency estimation, stream automata, linear map}
}

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  • Authors
  • C
  • Czumaj, Artur
  • G
  • Ganguly, Sumit
  • K
  • Kaufman, Tali
  • L
  • Litsyn, Simon
  • M
  • Muthukrishnan, S. Muthu
  • R
  • Rubinfeld, Ronitt
  • S
  • Sohler, Christian
  • X
  • Xie, Ning

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