On the variance of the external path length in a symmetric digital trie
Discrete Applied Mathematics - Combinatorics and complexity
Autocorrelation on words and its applications: analysis of suffix trees by string-ruler approach
Journal of Combinatorial Theory Series A
Mellin transforms and asymptotics: harmonic sums
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Faster IP lookups using controlled prefix expansion
SIGMETRICS '98/PERFORMANCE '98 Proceedings of the 1998 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Analytical depoissonization and its applications
Theoretical Computer Science
Selected papers on analysis of algorithms
Selected papers on analysis of algorithms
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
Some results on tries with adaptive branching
Theoretical Computer Science
On the number of full levels in tries
Random Structures & Algorithms
(Un)expected behavior of digital search tree profile
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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Tries and suffix trees are the most popular data structures on words. Tries were introduced in 1960 by Fredkin as an efficient method for searching and sorting digital data. Since then myriad of novel trie applications were found such as dynamic hashing, conflict resolution algorithms, leader election algorithms, IP addresses lookup, coding, polynomial factorization, Lempel-Ziv compression schemes, and so on. Furthermore, various analyses of tries reveal new fundamental properties of strings appearing in those applications. Parameters of interest are the (partial) fillup level (the largest full level of the trie), shortest path, height (longest path), typical depth, and path length (sum of depths). All of these parameters are analyzed here in a unifying manner by studying the external and internal profiles. A profile of a tree at level k is the number of nodes (internal or external) at level k. We derive recurrences for both profiles and solve them asymptotically for various ranges of k when the strings stored in the trie are generated by a memoryless source (extension to a Markov source is possible). In particular, we present asymptotic results for the average profile, the variance and the limiting distribution. As consequences we find the height, shortest path, fillup level, and the depth. These results are derived here by methods of analytic algorithmics such as generating functions, Mellin transform, poissonization and depoissonization, and the saddle point method.