Multivariate Normal Limit Laws for the Numbers of Fringe Subtrees in $m$-ary Search Trees and Preferential Attachment Trees
نویسندگان
چکیده
منابع مشابه
Multivariate Normal Limit Laws for the Numbers of Fringe Subtrees in m-ary Search Trees and Preferential Attachment Trees
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 prove general limit theorems for sums of functions of subtrees of (random) binary search trees and random recursive trees. The proofs use a new version of a representation by Devroye, and Stein’s method for both normal and Poisson approximation together with certain couplings. As a consequence, we give simple new proofs of the fact that the number of fringe trees of size k = kn in the binary...
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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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We consider sums of functions of subtrees of a random binary search tree, and obtain general laws of large numbers and central limit theorems. These sums correspond to random recurrences of the quicksort type, Xn L = XIn+X ′ n−1−In+Yn, n ≥ 1, where In is uniformly distributed on {0, 1, . . . , n− 1}, Yn is a given random variable, Xk L = X ′ k for all k, and given In, XIn and X ′ n−1−In are ind...
متن کاملStein Couplings to Show Limit Laws for Fringe Trees
The binary search tree or Quicksort is the most used of all sorting algorithm, since it is both fast and simple. The random recursive tree is another extensively studied random tree. We have examined fringe trees in these two types of random trees, since the study of such subtrees appears to be an effective approach towards defining characteristics also of the whole tree. By using a representat...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/6374