HOARES SELECTION ALGORITHM - A MARKOV-CHAIN APPROACH

We obtain bounds for the distribution of the number of comparisons nee ded by Hoare's randomized selection algorithm FIND and give a new proo f for Grubel and Rosler's (1996) result on the convergence of this dis tribution. Our approach is based on the construction and analysis of a suitable associated Markov chain. Some numerical results fur the quan tiles 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 x n comparisons to find the medi an of S.