Fringe trees, Crump–Mode–Jagers branching processes and $m$-ary search trees
نویسندگان
چکیده
منابع مشابه
Fringe trees, Crump–Mode–Jagers branching processes and m-ary search trees
This survey studies asymptotics of random fringe trees and extended fringe trees in random trees that can be constructed as family trees of a Crump–Mode–Jagers branching process, stopped at a suitable time. This includes random recursive trees, preferential attachment trees, fragmentation trees, binary search trees and (more generally) m-ary search trees, as well as some other classes of random...
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Let m ≥ 3 be an integer. The so-called m-ary search tree is a discrete time Markov chain which is very popular in theoretical computer science, modelling famous algorithms used in searching and sorting. This random process satisfies a well-known phase transition: when m ≤ 26, the asymptotic behavior of the process is Gaussian, but for m ≥ 27 it is no longer Gaussian and a limit W of a complex-v...
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We study fringe subtrees of random m-ary search trees and of preferential attachment trees, by putting them in the context of generalised Pólya urns. In particular we show that for the random m-ary search trees with m ≤ 26 and for the linear preferential attachment trees, the number of fringe subtrees that are isomorphic to an arbitrary fixed tree T converges to a normal distribution; more gene...
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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 6 m 6 13 but becomes of higher order when m > 14. Surprisingly, the corresponding asymptotic correl...
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A random m-ary leach tree is constructed from a random permutation of 1, . . . , n. A la of large numbers is obtained for the height Hn of these trees by applying the theory of branching random alks . In particular, it is sho n that Ha/log n y in probability as n ---~ oo, here y = y(m) is a constant depending upon m only. Interestingly, as m ---~ 00 , y(m) is asymptotic to 1/log m, the coeffici...
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ژورنال
عنوان ژورنال: Probability Surveys
سال: 2017
ISSN: 1549-5787
DOI: 10.1214/16-ps272