Abstract
Analysis of Algorithms 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.
Highlights
Helmut ProdingerDigital search trees with m trees: Level polynomials and insertion costs
The following sentences from our own Prodinger (1995), which never appeared in a proper journal, can be reproduced here almost verbatim: A DST is constructed like a binary search tree, but the decision to go down to the left or right is done according to the representation of the key as a binary string of bits
In order to study the average search costs in a DST built from n random data, the polynomial Hn(u), which has as the coefficient of uk the expected number of nodes on this level, is studied
Summary
Digital search trees with m trees: Level polynomials and insertion costs. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2011, Vol 13 no. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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