Profile of tries

Authors:
G. Park;H.-K. Hwang;P. Nicodème;W. Szpankowski
Affiliations:
Department of Computer Science, State University of New York at Geneseo, Geneseo;Institute of Statistical Science, Academia Sinica, Taipei, Taiwan;Laboratory LIX, École polytechnique, Palaiseau Cedex, France;Department of Computer Sciences, Purdue University, West Lafayette, Indiana
Venue:
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Year:
2008

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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.