Основные понятия
Efficiently compute rotation distance between binary trees with rank constraints.
Аннотация
This study delves into the computation of rotation distance between binary trees with rank constraints. It introduces the concept of rank-bounded rotation distance and presents algorithms for computing it efficiently. The content is structured as follows:
- Introduction to Rotation Distance in Binary Trees
- Preliminaries on Binary Trees and Tree Permutations
- Characterization of Rotations Using Transpositions
- Computing Skew Rotation Distance for Rank 1 Trees
- Analysis of Paths in the Rotation Graphs
- Height Restricted Paths and Tree Polynomials Discussion
The study provides insights into the combinatorial and algorithmic aspects of rotation distance problems, focusing on skew trees and their associated permutations.
Статистика
Computing the skew rotation distance can be done in O(n^2) time.
The number of tree transpositions on n elements is (n - 1)^2.
The number of 1-transpositions on n elements is also (n - 1)^2.
Цитаты
"Every full binary tree with n internal nodes can be converted to a right comb tree with at most 2n - 2 rotations."
"A particularly important view of the computational problem is viewing it as a shortest path problem in an associated graph."
"The algorithm finds the optimal number of swaps to transform one binary string to another efficiently."