Hoare's selection algorithm: A Markov chain approach

Hoare's selection algorithm: A Markov chain approach

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Article ID: iaor1999385
Country: United Kingdom
Volume: 35
Issue: 1
Start Page Number: 36
End Page Number: 45
Publication Date: Mar 1998
Journal: Journal of Applied Probability
Authors:
Keywords: markov processes
Abstract:

We obtain bounds for the distribution of the number of comparisons needed by Hoare's randomized selection algorithm FIND and give a new proof for Grübel and Rösler's result on the convergence of this distribution. Our approach is based on the construction and analysis of a suitable associated Markov chain. Some numerical results for the quantiles of the limit distributions are included, leading for example to the statement that, for a set S with n elements and n large, FIND will need with probability 0.9 about 4.72 × n comparisons to find the median of S.

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