Building uniformly random subtrees
نویسندگان
چکیده
منابع مشابه
Limit Laws for Sums of Functions of Subtrees of Random Binary Search Trees
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 کاملSolution of in - class exercise 1 : Bounding a sequence
Induction step. Let n 2 and suppose that the lemma holds for all insertion permutations of size strictly less than n. Let π = (π(1), . . . , π(n)) be a permutation drawn uniformly at random from Sn. The rst element π(1) will become the root of the tree Tπ. Since the distribution of π(1) is u.a.r. from [n], the root of the tree is chosen uniformly at random, as required by the construction of ~ ...
متن کاملGenerating rooted trees of m nodes uniformly at random
A rooted tree is an ordinary tree with an equivalence condition: two trees are the same if and only if one can be transformed into the other by reordering subtrees. In this paper, we construct a bijection and use it to generate rooted trees (or forests) of any specified nodecount m uniformly at random. As an application, we see that in [6] Raddum and Semaev propose a technique to solve systems ...
متن کاملAlmost sure asymptotics for the random binary search tree
Consider the complete rooted binary tree T. We construct a sequence Tn, n = 1, 2, . . . of subtrees of T recursively as follows. T1 consists only of the root. Given Tn, we choose a leaf u uniformly at random from the set of all leaves of Tn and add its two children to the tree to create Tn+1. Thus Tn+1 consists of Tn and the children u1, u2 of u, and contains in total 2n+ 1 nodes, including n+ ...
متن کاملUsing Stein’s Method to Show Poisson and Normal Limit Laws for Fringe Subtrees
We consider sums of functions of fringe subtrees of binary search trees and random recursive trees (of total size n). The use of Stein’s method and certain couplings allow provision of simple proofs showing that in both of these trees, the number of fringe subtrees of size k < n, where k → ∞, can be approximated by a Poisson distribution. Combining these results and another version of Stein’s m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Random Struct. Algorithms
دوره 24 شماره
صفحات -
تاریخ انتشار 2004