Trie partitioning process: limiting distributions
CAAP '86 Proceedings of the 11th colloquium on trees in algebra and programming
A characterization of digital search trees from the successful search viewpoint
Theoretical Computer Science
Mellin transforms and asymptotics: harmonic sums
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Asymptotic behavior of the Lempel-Ziv parsing scheme and digital search trees
Theoretical Computer Science - Special volume on mathematical analysis of algorithms (dedicated to D. E. Knuth)
Analytical depoissonization and its applications
Theoretical Computer Science
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Novel architectures for P2P applications: the continuous-discrete approach
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Profile of tries
Analytic Combinatorics
SIAM Journal on Computing
Analysis of digital tries with Markovian dependency
IEEE Transactions on Information Theory
Average profile and limiting distribution for a phrase size in the Lempel-Ziv parsing algorithm
IEEE Transactions on Information Theory
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A digital search tree (DST) is a fundamental data structure on words that finds various applications from the popular Lempel-Ziv@?78 data compression scheme to distributed hash tables. The profile of a DST measures the number of nodes at the same distance from the root; it depends on the number of stored strings and the distance from the root. Most parameters of DST (e.g., depth, height, fillup) can be expressed in terms of the profile. We study here asymptotics of the average profile in a DST built from sequences generated independently by a memoryless source. After representing the average profile by a recurrence, we solve it using a wide range of analytic tools. This analysis is surprisingly demanding but once it is carried out it reveals an unusually intriguing and interesting behavior. The average profile undergoes phase transitions when moving from the root to the longest path: at first it resembles a full tree until it abruptly starts growing polynomially and oscillating in this range. These results are derived by methods of analytic combinatorics such as generating functions, Mellin transform, poissonization and depoissonization, the saddle point method, singularity analysis and uniform asymptotic analysis.