Abstract
The profile of a trie, the most popular data structures on words,is a parameter that represents the number of nodes (either internal or external) with the same distance to the root. Several, if not all, trie parameters such as height, size, depth, shortest path, and fill-up level can be uniformly analyzed through the (external and internal) profiles. The analysis of profiles is surprisingly arduous but once it is carried out it reveals unusually intriguing and interesting behavior. We present a detailed study of the distribution of the profiles in a trie built over strings generated by a memoryless source (extension to Markov sources is possible). Our results are derived by methods of analytic algorithmics such as generating functions, Mellin transform, Poissonization and de-Poissonization, the saddle-point method, singularity analysis and uniform asymptotic analysis.
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Park, G., Hwang, H.K., Nicodème, P., Szpankowski, W. (2008). Profile of Tries. In: Laber, E.S., Bornstein, C., Nogueira, L.T., Faria, L. (eds) LATIN 2008: Theoretical Informatics. LATIN 2008. Lecture Notes in Computer Science, vol 4957. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78773-0_1
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DOI: https://doi.org/10.1007/978-3-540-78773-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78772-3
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