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The complexity of the algorithm Radix Selection is considered for independentdata generated from a Markov source. The complexity is measured by the numberof bucket operations required and studied as a stochastic process indexed bythe ranks; also the case of a uniformly chosen rank is considered. The ordersof mean and variance of the complexity and limit theorems are derived. We findweak convergence of the appropriately normalized complexity towards a Gaussianprocess with explicit mean and covariance functions (in the space D[0,1] ofcadlag functions on [0,1] with the Skorokhod metric) for uniform data and theasymmetric Bernoulli model. For uniformly chosen ranks and uniformlydistributed data the normalized complexity was known to be asymptoticallynormal. For a general Markov source (excluding the uniform case) we find thatthis complexity is less concentrated and admits a limit law with non-normallimit distribution.

Analysis of radix selection on Markov sources