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An analytic approach to the asymptotic variance of trie statistics and related structures
, 2013
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Renewal theory for the analysis of tries and strings (Extended Abstract)
, 2010
"... We give a survey of a number of simple applications of renewal theory to problems on random strings, in particular to tries and Khodak and Tunstall codes. ..."
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We give a survey of a number of simple applications of renewal theory to problems on random strings, in particular to tries and Khodak and Tunstall codes.
Analysis of radix selection on Markov sources
, 2014
"... The complexity of the algorithm Radix Selection is considered for independent data generated from a Markov source. The complexity is measured by the number of bucket operations required and studied as a stochastic process indexed by the ranks; also the case of a uniformly chosen rank is considered. ..."
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The complexity of the algorithm Radix Selection is considered for independent data generated from a Markov source. The complexity is measured by the number of bucket operations required and studied as a stochastic process indexed by the ranks; also the case of a uniformly chosen rank is considered. The orders of mean and variance of the complexity and limit theorems are derived. We find weak convergence of the appropriately normalized complexity towards a Gaussian process with explicit mean and covariance functions (in the space D[0,1] of càdlàg functions on [0,1] with the Skorokhod metric) for uniform data and the asymmetric Bernoulli model. For uniformly chosen ranks and uniformly distributed data the normalized complexity was known to be asymptotically normal. For ageneral Markov source (excludingthe uniform case) we findthat this complexity is less concentrated and admits a limit law with nonnormal limit distribution.