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Digital search trees with m trees: Level polynomials and insertion costs

Abstract : We adapt a novel idea of Cichon's related to Approximate Counting to the present instance of Digital Search Trees, by using m (instead of one) such trees. We investigate the level polynomials, which have as coefficients the expected numbers of data on a given level, and the insertion costs. The level polynomials can be precisely described, thanks to formulae from q-analysis. The asymptotics of expectation and variance of the insertion cost are fairly standard these days and done with Rice's method.
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Helmut Prodinger. Digital search trees with m trees: Level polynomials and insertion costs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2011, Vol. 13 no. 3 (3), pp.1--7. ⟨10.46298/dmtcs.557⟩. ⟨hal-00990489⟩

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