Trie partitioning process: limiting distributions
CAAP '86 Proceedings of the 11th colloquium on trees in algebra and programming
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
Limit laws for the height in PATRICIA tries
Journal of Algorithms - Analysis of algorithms
Some results on tries with adaptive branching
Theoretical Computer Science
Towards a complete characterization of tries
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
On the average depth of asymmetric LC-tries
Information Processing Letters
Partial fillup and search time in LC tries
ACM Transactions on Algorithms (TALG)
On the average depth of asymmetric LC-tries
Information Processing Letters
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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We study the asymptotic distribution of the fill-up level in a binary trie built over n independent strings generated by a biased memoryless source. The fill-up level is the number of full levels in a tree. A level is full if it contains the maximum allowable number of nodes (e.g., in a binary tree level k can have up to 2k nodes). The fill-up level finds many interesting applications, e.g., in the internet IP lookup problem and in the analysis of level compressed tries (LC tries). In this paper, we present a complete asymptotic characterization of the fill-up distribution. In particular, we prove that this distribution concentrates on one or two points around the most probably value k = ⌊log1/qn - log log log n + 1 + log log(p/q)⌋, where p q = 1 - p is the probability of generating the more likely symbol (while q = 1 - p is the probability of the less likely symbol). We derive our results by analytic methods such as generating functions, Mellin transform, the saddle point method, and analytic depoissonization. We also present some numerical verification of our results.