License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2011.428
URN: urn:nbn:de:0030-drops-30322
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2011/3032/
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McGregor, Andrew ; Rudra, Atri ; Uurtamo, Steve

Polynomial Fitting of Data Streams with Applications to Codeword Testing

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Abstract

Given a stream of $(x,y)$ points, we consider the problem of finding univariate polynomials that best fit the data. Over finite fields, this problem encompasses the well-studied problem of decoding Reed-Solomon codes while over the reals it corresponds to the well-studied polynomial regression problem.

We present one-pass algorithms for two natural problems: i) find the polynomial of a given degree $k$ that minimizes the error and ii) find the polynomial of smallest degree that interpolates through the points with at most a given error bound. We consider a range of error models including the average error per point, the maximum error, and the number of points that are not fitted exactly. Many of our results apply to both the reals and finite fields. As a consequence we also solve an open question regarding the tolerant testing of codes in the data stream model.

BibTeX - Entry

@InProceedings{mcgregor_et_al:LIPIcs:2011:3032,
  author =	{Andrew McGregor and Atri Rudra and Steve Uurtamo},
  title =	{{Polynomial Fitting of Data Streams with Applications to Codeword Testing}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011) },
  pages =	{428--439},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Thomas Schwentick and Christoph D{\"u}rr},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2011/3032},
  URN =		{urn:nbn:de:0030-drops-30322},
  doi =		{10.4230/LIPIcs.STACS.2011.428},
  annote =	{Keywords: Streaming, Polynomial Interpolation, Polynomial Regression}
}

Keywords: Streaming, Polynomial Interpolation, Polynomial Regression
Collection: 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)
Issue Date: 2011
Date of publication: 11.03.2011

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