Digital search trees revisited
SIAM Journal on Computing
Some further results on digital search trees
International Colloquium on Automata, Languages and Programming on Automata, languages and programming
Some results on V-ary asymmetric tries
Journal of Algorithms
Elements of information theory
Elements of information theory
Improved behaviour of tries by adaptive branching
Information Processing Letters
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Analytic variations on bucket selection and sorting
Acta Informatica
Communications of the ACM
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Trie Partitioning Process: Limiting Distributions
CAAP '86 Proceedings of the 11th Colloquium on Trees in Algebra and Programming
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On the number of full levels in tries
Random Structures & Algorithms
Towards a complete characterization of tries
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Partial fillup and search time in LC tries
ACM Transactions on Algorithms (TALG)
Analysis of a class of tries with adaptive multi-digit branching
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Hi-index | 5.23 |
We study a modification of digital trees (or tries) with adaptive multi-digit branching. Such tries can dynamically adjust degrees of their nodes by choosing the number of digits to be processed per lookup. While we do not specify any particular method for selecting the degrees of nodes, we assume that such selection can be accomplished by examining the number of strings remaining in each sub-tree, and/or estimating parameters of the input distribution. We call this class of digital trees adaptive multi-digit tries (or AMD-tries) and provide a preliminary analysis of their expected behavior in a memoryless model. We establish the following results: (1) there exist AMD-tries attaining a constant expected time of a successful search; (2) there exist AMD-tries consuming a linear (in the number of strings inserted) amount of space; (3) both constant search time and linear space usage can be attained if the (memoryless) source is symmetric. We accompany our analysis with a brief survey of several known types of adaptive trie structures, and show how our analysis extends (and/or complements) previous results.