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 Author, Editor(s)
 Author(s): Doerr, Benjamin Gnewuch, Michael Srivastav, Anand dblp dblp dblp Not MPG Author(s): Gnewuch, Michael Srivastav, Anand
 BibTeX cite key*: Doerr2005gitter

 Title
 Title*: Bounds and Constructions for the Star-Discrepancy via Delta-Covers

 Journal
 Journal Title*: Journal of Complexity Journal's URL: http://www.sciencedirect.com/science/journal/0885064X Download URL for the article: Language: English

 Publisher
 Publisher's Name: Elsevier Publisher's URL: http://www.elsevier.com/ Publisher's Address: Amsterdam, The Netherlands ISSN: 0885-064X

 Vol, No, pp, Date
 Volume*: 21 Number: 5 Publishing Date: October 2005 Pages*: 691-709 Number of VG Pages: 39 Page Start: Page End: Sequence Number: DOI:

 Note: (LaTeX) Abstract: For numerical integration in higher dimensions, bounds for the star-dis\-cre\-pan\-cy with polynomial dependence on the dimension $d$ are desirable. Furthermore, it is still a great challenge to give construction methods for low-discrepancy point sets. In this paper we give upper bounds for the star-discrepancy and its inverse for subsets of the $d$-di\-men\-sio\-nal unit cube. They improve known results. In particular, we determine the usually only implicitly given constants. The bounds are based on the construction of nearly optimal $\delta$-covers of anchored boxes in the $d$-dimensional unit cube. We give an explicit construction of low-discrepancy points with a derandomized algorithm. The running time of the algorithm, which is exponentially in $d$, is discussed in detail and comparisons with other methods are given. URL for the Abstract: Categories, Keywords: covering number, derandomization, low-discrepancy point sets, probabilistic methods, star-discrepancy HyperLinks / References / URLs: Copyright Message: Personal Comments: Download Access Level: Intranet

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 MPG Unit: Max-Planck-Institut für Informatik MPG Subunit: Algorithms and Complexity Group Appearance: MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort

BibTeX Entry:

@ARTICLE{Doerr2005gitter,
AUTHOR = {Doerr, Benjamin and Gnewuch, Michael and Srivastav, Anand},
TITLE = {Bounds and Constructions for the Star-Discrepancy via Delta-Covers},
JOURNAL = {Journal of Complexity},
PUBLISHER = {Elsevier},
YEAR = {2005},
NUMBER = {5},
VOLUME = {21},
PAGES = {691--709},