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
Compressed dynamic tries with applications to LZ-compression in sublinear time and space
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Analysis of a class of tries with adaptive multi-digit branching
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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Level-Compressed (in short LC) tries were introduced by Andersson and Nilsson in 1993. They are compacted versions of tries in which, from the top down, maximal height complete subtrees are level compressed. We show that when the input consists of n independent strings with independent Bernoulli (p) bits, p ≠ 1/2, then the expected depth of a typical node is in probability asymptotic to $${{\rm log\,\,log}\,\,n} \over {\rm log}\,\, \left(1 - {{\cal H} \over {\cal H} - \infty}\right)$$ where H - p log p - (1 - p) log (1 - p) is the Shannon entropy of the source, and H-∞ = log (1 / min(p, 1 - p)). The height is in probability asymptotic to $${{\rm log}\,\,n}\,\, \over {\cal H}_2$$ where H2 = log(1/(p2 + (1-p)2)). © 2005 Wiley Periodicals, Inc. Random Struct. Alg., 2005