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Blunck, Henrik ; Vahrenhold, Jan

In-Place Randomized Slope-Selection

06091.VahrenholdJan.Paper.839.pdf (0.2 MB)


Slope selection is a well-known algorithmic tool used in the context of computing robust estimators for fitting a line to a collection $mathcal{P}$ of $n$ points in the plane. We demonstrate that it is possible to perform slope selection in expected $mathcal{O}(n log n)$ time using only constant extra space in addition to the space needed for representing the input. Our solution is based upon a space-efficient variant of Matouv{s}ek's randomized interpolation search, and we believe that the techniques developed in this paper will prove helpful in the design of space-efficient randomized algorithms using samples. To underline this, we also sketch how to compute the repeated median line estimator in an in-place setting.

BibTeX - Entry

  author =	{Henrik Blunck and Jan Vahrenhold},
  title =	{In-Place Randomized Slope-Selection},
  booktitle =	{Data Structures},
  year =	{2006},
  editor =	{Lars Arge and Robert Sedgewick and Dorothea Wagner},
  number =	{06091},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: In-Place Algorithms, Slope Selection}

Keywords: In-Place Algorithms, Slope Selection
Seminar: 06091 - Data Structures
Issue Date: 2006
Date of publication: 30.11.2006

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