Low Discrepancy Sets Yield Approximate Min-Wise Independent Permutation Families View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1999

AUTHORS

Michael Saks , Aravind Srinivasan , Shiyu Zhou , David Zuckerman

ABSTRACT

Motivated by a problem of filtering near-duplicate Web documents, Broder, Charikar, Frieze & Mitzenmacher defined the following notion of ε-approximate min-wise independent permutation families [2]. A multiset \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{F}$\end{document} of permutations of {0,1, ... , n–1} is such a family if for all K ⊆ {0,1, ..., n–1} and any x ∈ K, a permutation π chosen uniformly at random form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{F}$\end{document} statisfies\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$| Pr[min\{\pi(K)\} = \pi(x)] - \frac{1}{|K|}| \leq \frac{\epsilon}{|K|}$\end{document}.We show connections of such families with low discrepancy sets for geometric rectangles, and give explicit constructions of such families \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{F}$\end{document} of size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n ^{O(\sqrt{\log n})}$\end{document} for ε = 1 / nθ(1), improving upon the previously best-known bound of Indyk [4]. We also present polynomial-size constructions when the min-wise condition is required only for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vert K\vert \leq 2 ^{O(\log^{2/3} n)}$\end{document}, with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \epsilon \geq 2 ^{-O(\log^{2/3} n)}$\end{document}. More... »

PAGES

11-15

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-540-48413-4_2

DOI

http://dx.doi.org/10.1007/978-3-540-48413-4_2

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1044928628


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