Probabilistic Analysis of Radix Algorithms on Markov Sources

This book is about the analysis of radix sort, radix select and the path length of digital trees under a stochastic input assumption known as the Markov model. The main results are about the asymptotic expansions of mean and variance as well as a central limit theorem for the complexity of radix sort and the path length of tries, PATRICIA tries and digital search trees. Concerning radix select, a variety of different models for ranks are discussed including a law of large numbers for the worst case behavior, a limit theorem for the grand averages model and the first order asymptotic of the average complexity in the quantile model. Some of the results are achieved by moment transfer techniques, the limit laws are based on a novel use of the contraction method adjusted to systems of stochastic recurrences.