More on Symmetric Brothers of a Node in a Perfect Binary Tree
Xingbo Wang *
Department of Mechatronic Engineering, Foshan University, Foshan City, PRC, 528000, China and Guangdong Engineering Center of Information Security for Intelligent Manufacturing System, Foshan City, PRC, China.
*Author to whom correspondence should be addressed.
Abstract
The paper makes an extensive study on the symmetric brothers of a node in a perfect binary tree. Through proving several new properties of the symmetric brothers of a node, it reveals how the symmetric brothers and the symmetric ancestors distribute on the tree and how they are beneficial for designing a searching algorithm of special purpose. Detail mathematical reasoning and proofs are shown together with concrete examples to demonstrate the mathematical traits. The paper is helpful for designing algorithms in blind search related aspects.
Keywords: Binary tree, ancestor, symmetric brother, distribution, geometric progression