{"@context":"https:\/\/schema.org\/","@type":"PublicationVolume","@id":"#volume712","volumeNumber":8341,"name":"Dagstuhl Seminar Proceedings, Volume 8341","dateCreated":"2008-11-25","datePublished":"2008-11-25","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"Periodical","@id":"#series119","name":"Dagstuhl Seminar Proceedings","issn":"1862-4405","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume712"},"hasPart":[{"@type":"ScholarlyArticle","@id":"#article2195","name":"08341 Abstracts Collection \u2013 Sublinear Algorithms","abstract":"From August 17 to August 22, 2008, the Dagstuhl Seminar 08341 ``Sublinear Algorithms'' was held in the International Conference and Research Center (IBFI),\r\nSchloss Dagstuhl.\r\nDuring the seminar, several participants presented their current\r\nresearch, and ongoing work and open problems were discussed. Abstracts of\r\nthe presentations given during the seminar as well as abstracts of\r\nseminar results and ideas are put together in this paper. The first section\r\ndescribes the seminar topics and goals in general.\r\nLinks to extended abstracts or full papers are provided, if available.","keywords":["Sublinear algorithms","property testing","data streaming","graph algorithms","approximation algorithms"],"author":[{"@type":"Person","name":"Czumaj, Artur","givenName":"Artur","familyName":"Czumaj"},{"@type":"Person","name":"Muthukrishnan, S. Muthu","givenName":"S. Muthu","familyName":"Muthukrishnan"},{"@type":"Person","name":"Rubinfeld, Ronitt","givenName":"Ronitt","familyName":"Rubinfeld"},{"@type":"Person","name":"Sohler, Christian","givenName":"Christian","familyName":"Sohler"}],"position":1,"pageStart":1,"pageEnd":19,"dateCreated":"2008-11-25","datePublished":"2008-11-25","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Czumaj, Artur","givenName":"Artur","familyName":"Czumaj"},{"@type":"Person","name":"Muthukrishnan, S. Muthu","givenName":"S. Muthu","familyName":"Muthukrishnan"},{"@type":"Person","name":"Rubinfeld, Ronitt","givenName":"Ronitt","familyName":"Rubinfeld"},{"@type":"Person","name":"Sohler, Christian","givenName":"Christian","familyName":"Sohler"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08341.1","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume712"},{"@type":"ScholarlyArticle","@id":"#article2196","name":"08341 Executive Summary \u2013 Sublinear Algorithms","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.","keywords":["Sublinear algorithms","property testing","data streaming","graph algorithms","approximation algorithms"],"author":[{"@type":"Person","name":"Czumaj, Artur","givenName":"Artur","familyName":"Czumaj"},{"@type":"Person","name":"Muthukrishnan, S. Muthu","givenName":"S. Muthu","familyName":"Muthukrishnan"},{"@type":"Person","name":"Rubinfeld, Ronitt","givenName":"Ronitt","familyName":"Rubinfeld"},{"@type":"Person","name":"Sohler, Christian","givenName":"Christian","familyName":"Sohler"}],"position":2,"pageStart":1,"pageEnd":2,"dateCreated":"2008-11-25","datePublished":"2008-11-25","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Czumaj, Artur","givenName":"Artur","familyName":"Czumaj"},{"@type":"Person","name":"Muthukrishnan, S. Muthu","givenName":"S. Muthu","familyName":"Muthukrishnan"},{"@type":"Person","name":"Rubinfeld, Ronitt","givenName":"Ronitt","familyName":"Rubinfeld"},{"@type":"Person","name":"Sohler, Christian","givenName":"Christian","familyName":"Sohler"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08341.2","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume712"},{"@type":"ScholarlyArticle","@id":"#article2197","name":"Breaking the $\\epsilon$-Soundness Bound of the Linearity Test over GF(2)","abstract":"For Boolean functions that are $epsilon$-far from the set of linear functions, \r\nwe study the lower bound on the rejection probability (denoted by $extsc{rej}(epsilon)$) of the linearity test suggested by Blum, Luby and Rubinfeld. \r\nThis problem is arguably the most fundamental and extensively studied problem in property testing of Boolean functions. \r\n\r\nThe previously best bounds for $extsc{rej}(epsilon)$ were obtained by Bellare,\r\nCoppersmith, H{{a}}stad, Kiwi and Sudan. They used Fourier analysis\r\nto show that $\textsc{rej}(epsilon) geq e$ for every $0 leq epsilon leq\r\nfrac{1}{2}$. They also conjectured that this bound might not be tight for\r\n$epsilon$'s which are close to $1\/2$. In this paper we show that this indeed is\r\nthe case. Specifically, we improve the lower bound of $\textsc{rej}(epsilon) geq\r\nepsilon$ by an additive constant that depends only on $epsilon$:\r\n$extsc{rej}(epsilon) geq epsilon + min {1376epsilon^{3}(1-2epsilon)^{12},\r\nfrac{1}{4}epsilon(1-2epsilon)^{4}}$, for every $0 leq epsilon leq frac{1}{2}$.\r\nOur analysis is based on a relationship between $extsc{rej}(epsilon)$ and the\r\nweight distribution of a coset of the Hadamard code. We use both Fourier\r\nanalysis and coding theory tools to estimate this weight distribution.","keywords":["Linearity test","Fourier analysis","coding theory"],"author":[{"@type":"Person","name":"Kaufman, Tali","givenName":"Tali","familyName":"Kaufman"},{"@type":"Person","name":"Litsyn, Simon","givenName":"Simon","familyName":"Litsyn"},{"@type":"Person","name":"Xie, Ning","givenName":"Ning","familyName":"Xie"}],"position":3,"pageStart":1,"pageEnd":0,"dateCreated":"2008-11-25","datePublished":"2008-11-25","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Kaufman, Tali","givenName":"Tali","familyName":"Kaufman"},{"@type":"Person","name":"Litsyn, Simon","givenName":"Simon","familyName":"Litsyn"},{"@type":"Person","name":"Xie, Ning","givenName":"Ning","familyName":"Xie"}],"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08341.3","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume712"},{"@type":"ScholarlyArticle","@id":"#article2198","name":"Lower bound for estimating frequency for update data streams","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, \r\n$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: \r\n\r\n\r\norm{hat{f} (sigma)- f(sigma)} le epsilon \r\norm{f(sigma)}_p\r\n\r\nFor $p=1$ and $2$, there are randomized algorithms known with space bound $\tilde{O}(epsilon^{-p})$. A space lower bound of $Omega(epsilon^{-1} log (nepsilon))$ is also known. However, the deterministic space upper bound is $\tilde{O}(epsilon^{-2})$. \r\n\r\nIn 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 $epsilon < 1\/4$.\r\n\r\nThe 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.","keywords":["Data stream","lower bound","frequency estimation","stream automata","linear map"],"author":{"@type":"Person","name":"Ganguly, Sumit","givenName":"Sumit","familyName":"Ganguly"},"position":4,"pageStart":1,"pageEnd":15,"dateCreated":"2008-11-25","datePublished":"2008-11-25","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode","copyrightHolder":{"@type":"Person","name":"Ganguly, Sumit","givenName":"Sumit","familyName":"Ganguly"},"copyrightYear":"2008","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/DagSemProc.08341.4","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":"#volume712"}]}