Type of Publication:  Preprint 
Publication status:  Published 
Author:  Eckhardt, Stefan; Kosub, Sven; Nowak, Johannes 
Year of publication:  2020 
ArXivID:  arXiv:2003.04101 
Summary: 
Tries are general purpose data structures for information retrieval. The most significant parameter of a trie is its height H which equals the length of the longest common prefix of any two string in the set A over which the trie is built. Analytical investigations of random tries suggest that Exp(H)\in O(log A)), although H is unbounded in the worst case. Moreover, sharp results on the distribution function of H are known for many different random string sources. But because of the inherent weakness of the modeling behind averagecase analysisanalyses being dominated by random datathese results can utterly explain the fact that in many practical situations the trie height is logarithmic. We propose a new semirandom string model and perform a smoothed analysis in order to give a mathematically more rigorous explanation for the practical findings. The perturbation functions which we consider are based on probabilistic finite automata (PFA) and we show that the transition probabilities of the representing PFA completely characterize the asymptotic growth of the smoothed trie height. Our main result is of dichotomous naturelogarithmic or unboundedand is certainly not surprising at first glance, but we also give quantitative upper and lower bounds, which are derived using multivariate generating function in order to express the computations of the perturbing PFA. A direct consequence is the logarithmic trie height for edit perturbations(i.e., random insertions, deletions and substitutions).

Subject (DDC):  004 Computer Science 
Keywords:  Analysis of Algorithms, Trie 
Bibliography of Konstanz:  Yes 
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ECKHARDT, Stefan, Sven KOSUB, Johannes NOWAK, 2020. Smoothed Analysis of Trie Height by Starlike PFAs
@unpublished{Eckhardt20200309T12:55:36ZSmoot55838, title={Smoothed Analysis of Trie Height by Starlike PFAs}, year={2020}, author={Eckhardt, Stefan and Kosub, Sven and Nowak, Johannes} }
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