2016
DOI: 10.1002/rsa.20659
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Dependence and phase changes in random m‐ary search trees

Abstract: We study the joint asymptotic behavior of the space requirement and the total path length (either summing over all root-key distances or over all root-node distances) in random m-ary search trees. The covariance turns out to exhibit a change of asymptotic behavior: it is essentially linear when 3 m 13, but becomes of higher order when m 14. Surprisingly, the corresponding asymptotic correlation coefficient tends to zero when 3 m 26, but is periodically oscillating for larger m, and we also prove asymptotic ind… Show more

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Cited by 1 publication
(28 citation statements)
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“…Theorem A. The covariance of the number of internal nodes and KPL in a random trie of n strings satisfies Cov(S n , K n ) ∼ nF [g (2) ](n),…”
Section: Shape Parametersmentioning
confidence: 99%
See 4 more Smart Citations
“…Theorem A. The covariance of the number of internal nodes and KPL in a random trie of n strings satisfies Cov(S n , K n ) ∼ nF [g (2) ](n),…”
Section: Shape Parametersmentioning
confidence: 99%
“…Next, again from (6) we see that M [h 1 (z); s] can be analytically continued to the vertical line (s) = −1 and has no singularities there. Thus, by shifting the line of integration in (10) and computing residues, we obtainC (z) ∼ zF [g (2) ](z), uniformly for z in a sector.…”
Section: Covariance and Correlation Coefficientmentioning
confidence: 99%
See 3 more Smart Citations