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Renewal theory in analysis of tries and strings
, 2009
"... We give a survey of a number of simple applications of renewal theory to problems on random strings and tries: insertion depth, size, insertion mode and imbalance of tries; variations for btries and Patricia tries; Khodak and Tunstall codes. ..."
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We give a survey of a number of simple applications of renewal theory to problems on random strings and tries: insertion depth, size, insertion mode and imbalance of tries; variations for btries and Patricia tries; Khodak and Tunstall codes.
Dependence and phase changes in randommary search trees
, 2015
"... We study the joint asymptotic behavior of the space requirement and the total path length (either summing over all rootkey distances or over all rootnode distances) in random mary search trees. The covariance turns out to exhibit a change of asymptotic behavior: it is essentially linear when 3 ..."
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We study the joint asymptotic behavior of the space requirement and the total path length (either summing over all rootkey distances or over all rootnode distances) in random mary search trees. The covariance turns out to exhibit a change of asymptotic behavior: it is essentially linear when 3 6 m 6 13 but becomes of higher order when m> 14. Surprisingly, the corresponding asymptotic correlation coefficient tends to zero when 3 6 m 6 26 but is periodically oscillating for largerm. Such a less anticipated phenomenon is not exceptional and we extend the results in two directions: one for more general shape parameters, and the other for other classes of random logtrees such as fringebalanced binary search trees and quadtrees. The methods of proof combine asymptotic transfer for the underlying recurrence relations with the contraction method.