Binary trees, fringe thickness and minimum path length
نویسندگان
چکیده
منابع مشابه
The Maximal Path Length of Binary Trees
We further refine the bounds on the path length of binary trees of a given size by considering not only the size of a binary tree, but also its height and fringe thickness (the difference between the length of a shortest root-to-leaf path and the height). We characterize the maximum path length binary trees of a given height, size, and fringe thickness. Using this characterization, we give an a...
متن کاملMinimal Path Length of Trees with Known Fringe
In this paper we continue the study of the path length of trees with known fringe as initiated by 1] and 2]. We compute the path length of the minimal tree with given number of leaves N and fringe for the case N=2. This complements the result of 2] that studied the case N=2. Our methods also yields a linear time algorithm for constructing the minimal tree when N=2.
متن کاملA Note on the Expected Path Length of Trees with Known Fringe
The path length of a tree, that is the sum of the lengths of all root-leaf paths, is an important measure of eeciency of the tree. The fringe of a tree is the diierence between the lengths of the longest path and the shortest path in the tree. The minimal and the maximal path length of trees with N leaves and given fringe have been well studied. In this paper, we initiate the study of the expec...
متن کاملLimit laws for functions of fringe trees for binary search trees and random recursive trees
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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ژورنال
عنوان ژورنال: RAIRO - Theoretical Informatics and Applications
سال: 1995
ISSN: 0988-3754,1290-385X
DOI: 10.1051/ita/1995290301711