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.
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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. https://doi.org/10.1007/11758471_6
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DOI: https://doi.org/10.1007/11758471_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34375-2
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