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A fundamental algorithm for selecting ranks from a finite subset of anordered set is Radix Selection. This algorithm requires the data to be given asstrings of symbols over an ordered alphabet, e.g., binary expansions of realnumbers. Its complexity is measured by the number of symbols that have to beread. In this paper the model of independent data identically generated from aMarkov chain is considered. The complexity is studied as a stochastic processindexed by the set of infinite strings over the given alphabet. The orders ofmean and variance of the complexity and, after normalization, a limit theoremwith a centered Gaussian process as limit are derived. This implies an analysisfor two standard models for the ranks: uniformly chosen ranks, also calledgrand averages, and the worst case rank complexities which are of interest incomputer science. For uniform data and the asymmetric Bernoulli model (i.e.memoryless sources), we also find weak convergence for the normalized processof complexities when indexed by the ranks while for more general Markov sourcesthese processes are not tight under the standard normalizations.

Process convergence for the complexity of Radix Selection on Markov sources