Digital search trees revisited
SIAM Journal on Computing
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
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
The practical significance of D.P. sort revisited
Information Processing Letters
Improved Behaviour of Tries by the "Symmetrization" of the Source
DCC '02 Proceedings of the Data Compression Conference
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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 each 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 (O(1)) expected time of a successful search; 2) there exist AMD-tries consuming a linear (O(n), n is 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) the previous results.