In-Place Randomized Slope-Selection

Authors Henrik Blunck, Jan Vahrenhold

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Henrik Blunck
Jan Vahrenhold

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Henrik Blunck and Jan Vahrenhold. In-Place Randomized Slope-Selection. In Data Structures. Dagstuhl Seminar Proceedings, Volume 6091, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


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.
  • In-Place Algorithms
  • Slope Selection


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