Analysis of algorithms by the contraction method: additive and max-recursive sequences

In the first part of this paper we give an introduction to the contraction method for the analysis of additive recursive sequences of divide and conquer type. Recently some general limit theorems have been obtained by this method based on a general transfer theorem. This allows to conclude from the recursive structure and the asymptotics of first moment(s) the limiting distribution. In the second part we extend the contraction method to max-recursive sequences. We obtain a general existence and uniqueness result for solutions of stochastic equations including maxima and sum terms. We finally derive a general limit theorem for max-recursive sequences of the divide and conquer type.