On the average depth of asymmetric LC-tries

Andersson and Nilsson have already shown that the average depth D n of random LC-tries is only Θ ( log ∗ n ) when the keys are produced by a symmetric memoryless process, and that D n = O ( log log n ) when the process is asymmetric. In this paper we refine the second estimate by showing that asympt...

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Bibliographic Details
Published inInformation processing letters Vol. 96; no. 3; pp. 106 - 113
Main Author Reznik, Yuriy A.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 15.11.2005
Elsevier Science
Elsevier Sequoia S.A
Subjects
Algorithmics. Computability. Computer arithmetics
Algorithms
Analysis of algorithms
Applied sciences
Computer science; control theory; systems
Data processing. List processing. Character string processing
Exact sciences and technology
Information retrieval
LC-tries
Mathematical analysis
Memory organisation. Data processing
Software
Studies
Theoretical computing
Tries
Information retrieval
Algorithms
Analysis of algorithms
Tries
LC-tries
Computer theory
Information processing
Probability distribution
Algorithm
LC tries
Algorithm analysis
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Summary:Andersson and Nilsson have already shown that the average depth D n of random LC-tries is only Θ ( log ∗ n ) when the keys are produced by a symmetric memoryless process, and that D n = O ( log log n ) when the process is asymmetric. In this paper we refine the second estimate by showing that asymptotically (with n → ∞ ): D n ∼ 1 η log log n , where n is the number of keys inserted in a trie, η = − log ( 1 − h / h − ∞ ) , h = − p log p − q log q is the entropy of a binary memoryless source with probabilities p, q = 1 − p ( p ≠ q ), and h − ∞ = − log min ( p , q ) .
ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2005.06.008