Partial match retrieval of multidimensional data
Journal of the ACM (JACM)
Trie partitioning process: limiting distributions
CAAP '86 Proceedings of the 11th colloquium on trees in algebra and programming
On the balance property of Patricia tries: external path length viewpoint
Theoretical Computer Science
On the variance of the external path length in a symmetric digital trie
Discrete Applied Mathematics - Combinatorics and complexity
Algorithms in C
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)
The variance of a partial match retrieval in a multidimensional symmetric trie
Random Structures & Algorithms
Continued fraction algorithms, functional operators, and structure constants
Theoretical Computer Science
Analytical depoissonization and its applications
Theoretical Computer Science
The analysis of hybrid trie structures
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Communications of the ACM
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Size and path length of Patricia tries: dynamical sources context
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
The Art of Computer Programming, 2nd Ed. (Addison-Wesley Series in Computer Science and Information
Laws of large numbers and tail inequalities for random tries and PATRICIA trees
Journal of Computational and Applied Mathematics - Special issue: Probabilistic methods in combinatorics and combinatorial optimization
Normal Limiting Distribution of the Size of Tries
Performance '87 Proceedings of the 12th IFIP WG 7.3 International Symposium on Computer Performance Modelling, Measurement and Evaluation
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We show that, for a certain class of probabilistic models, the number of internal nodes $S_n$ of a trie built from $n$ independent and identically distributed keys is concentrated around its mean, in the sense that $\Var S_n=\Oh(\EE S_n)$. Keys are sequences of symbols which may be taken from varying alphabets, and the choice of the alphabet from which the $k$th symbol is taken, as well as its distribution, may depend on all the preceding symbols. In the construction of the trie we also allow for bucket sizes greater than 1. The property that characterizes our models is the following: there is a constant $C$ such that for any word $v$ that may occur as a prefix of a key the size $S^v_n$ of a trie built from the suffixes of $n$ independent keys conditioned to have the common prefix $v$ has the property $\EE S^v_n\leq Cn$. This class of models contains memoryless and Markovian source models as well as the probabilistic dynamical source models that were recently introduced and thoroughly developed by Vallée [Algorithmica 29 (2001) 262–306], in particular the continued fraction source. Furthermore we study the external path length $L_n$, which obeys $\EE L_n=\Oh(n\ln n)$ and $\Var L_n=\Oh(n\ln^2 n)$.