Abstract
This paper is devoted to the well-known trie structure. We consider two basic parameters: depth of the leaves and height when the trie is formed with n items. We prove the convergence of their distributions and of their moments of any order when n → ∞ to a limit distribution. We exhibit the limits : a periodic distribution or a normal distribution. The results are given for uniform or biased data distributions for Bernoulli and Poisson models. Our reasoning is based on generating and characteristic functions. We make an extensive use of analytic functions and asymptotic methods.
Preview
Unable to display preview. Download preview PDF.
References
Ph. Flajolet and C. Puech, “Tree Structure for Partial Match Retrieval,” pp. 282–288 in Proc. 24-th I.E.E.E. Symp. on FOCS, (1983). To appear in JACM
R. Fagin, J. Nievergelt, N. Pippenger, and H.R. Strong, “Extendible Hashing:A Fast Access Method for Dynamic Files,” ACM TODS 4,3 pp. 315–344 (1979).
G. Fayolle, Ph. Flajolet, M. Hofri, and Ph. Jacquet, “Analysis of a Stack Algorithm for Random Multiple-Access Communication,” IEEE Trans. on Information Theory IT-31,2 pp. 244–254 (1985).
W. Feller, An Introduction to Probability Theory and its Applications, Wiley-third Edition-1971 (1957).
Ph. Flajolet, “On the Performance Evaluation of Extendible Hashing and Trie Searching,” Acta Informatica 20 pp. 345–369 (1983).
Ph. Flajolet, M. Régnier, and D. Sotteau, “Algebraic Methods for Trie Statistics,” Annals of Discrete Mathematics 25 pp. 145–188 (1985).
Ph. Flajolet, M. Regnier, and R. Sedgewick, Some Uses of the Mellin Transform Techniques in the Analysis of Algorithms, Springer NATO ASI SEr. F12, Combinatorial Algorithms on Words (1985).
Ph. Flajolet, M. Regnier, and R. Sedgewick, “Mellin Transform Techniques for the Analysis of Algorithms”, Monography in preparation, (1986).
Ph. Flajolet and N. Saheb, “Digital Search Trees and the Complexity of Generating an Exponentially Distributed Variate,” in Proc. Coll. on Trees in Algebra and Programming, Lecture Notes in Computer Science, L'Aquila (1983). to appear
Ph. Flajolet and J.M. Steyaert, “A Branching Process Arising in Dynamic Hashing, Trie Searching and Polynomial Factorization,” pp. 239–251 in Proceedings ICALP 82, Lecture Notes in Computer Science (1982).
Ph. Jacquet and M. Régnier, Limiting Distributions for Trie Parameters, in preparation 1985.
D. Knuth, The Art of Computer Programming, Addison-Wesley, Reading,Mass. (1973).
P.A. Larson, “Dynamic Hashing,” BIT 18 pp. 184–201 (1978).
W. Litwin, “Trie Hashing,” pp. 19–29 in Proc. ACM-SIGMOD Conf. on MOD., Ann Arbor, Mich. (1981).
J. Nievergelt, H. Hinterberger, and K.C. Sevcik, “The Grid-file: an Adaptable Symmetric Multi-Key File Structure,” ACM TODS 9,1 (1984).
N.E. Norlund, Vorlesungen Uber Differenzenrechnung, Chelsea Publishing Company (1954).
M. Régnier, “Evaluation des performances du hachage dynamique,” These de 3-eme cycle, Universite d'Orsay, (1983).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1986 Springer-Verlag
About this paper
Cite this paper
Jacquet, P., Regnier, M. (1986). Trie partitioning process: Limiting distributions. In: Franchi-Zannettacci, P. (eds) CAAP '86. CAAP 1986. Lecture Notes in Computer Science, vol 214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022669
Download citation
DOI: https://doi.org/10.1007/BFb0022669
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16443-2
Online ISBN: 978-3-540-39783-0
eBook Packages: Springer Book Archive