In-Place Randomized Slope Selection

  • Henrik Blunck
  • Jan Vahrenhold
Conference paper

DOI: 10.1007/11758471_6

Volume 3998 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Blunck H., Vahrenhold J. (2006) In-Place Randomized Slope Selection. In: Calamoneri T., Finocchi I., Italiano G.F. (eds) Algorithms and Complexity. CIAC 2006. Lecture Notes in Computer Science, vol 3998. Springer, Berlin, Heidelberg

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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