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 Author, Editor
 Editor(s): Arge, Lars Freivalds, Rusins dblp dblp Not MPII Editor(s): Arge, Lars Freivalds, Rusins
 BibTeX cite key*: DFKO06

 Title, Booktitle
 Title*: Unbiased Matrix Rounding Booktitle*: Algorithm theory - SWAT 2006 : 10th Scandinavian Workshop on Algorithm Theory

 Event, URLs
 URL of the conference: http://www.lumii.lv/swat URL for downloading the paper: Event Address*: Riga, Latvia Language: English Event Date* (no longer used): Organization: Event Start Date: 6 July 2006 Event End Date: 8 July 2006

 Publisher
 Name*: Springer URL: http://www.springer.de/ Address*: Berlin, Germany Type:

 Vol, No, Year, pp.
 Series: Lecture Notes in Computer Science
 Volume: 4059 Number: Month: Pages: 102-112 Year*: 2006 VG Wort Pages: 26 ISBN/ISSN: 978-3-540-35753-7 Sequence Number: DOI:

 (LaTeX) Abstract: We show several ways to round a real matrix to an integer one in such a way that the rounding errors in all rows and columns as well as the whole matrix are less than one. This is a classical problem with applications in many fields, in particular, statistics. We improve earlier solutions of different authors in two ways. For rounding $m \times n$ matrices, we reduce the runtime from $O( (m n)^2 )$ to $O(m n \log(m n))$. Second, our roundings also have a rounding error of less than one in all initial intervals of rows and columns. Consequently, arbitrary intervals have an error of at most two. This is particularly useful in the statistics application of controlled rounding. The same result can be obtained via (dependent) randomized rounding. This has the additional advantage that the rounding is unbiased, that is, for all entries $y_{ij}$ of our rounding, we have $E(y_{ij}) = x_{ij}$, where $x_{ij}$ is the corresponding entry of the input matrix. Download Access Level: MPG

 Correlation
 MPG Unit: Max-Planck-Institut für Informatik MPG Subunit: Algorithms and Complexity Group Audience: not specified Appearance: MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort

BibTeX Entry:

@INPROCEEDINGS{DFKO06,
AUTHOR = {Doerr, Benjamin and Friedrich, Tobias and Klein, Christian and Osbild, Ralf},
EDITOR = {Arge, Lars and Freivalds, Rusins},
TITLE = {Unbiased Matrix Rounding},
BOOKTITLE = {Algorithm theory - SWAT 2006 : 10th Scandinavian Workshop on Algorithm Theory},
PUBLISHER = {Springer},
YEAR = {2006},
VOLUME = {4059},
PAGES = {102--112},
SERIES = {Lecture Notes in Computer Science},