In-Place Randomized Slope Selection

  • Henrik Blunck
  • Jan Vahrenhold
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3998)


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 Matoušek’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.


Computational Geometry Robust Estimator Extra Space Global Cost Recursion Tree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Henrik Blunck
    • 1
  • Jan Vahrenhold
    • 1
  1. 1.Institut für InformatikWestfälische Wilhelms-Universität MünsterMünsterGermany

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