The Primes Ancestor Tree
This will be just a small theoretical article on the Primes Ancestor Tree. We will explore the possibility to label a generic tree in such way that it will be possible to verify if a node is an ancestor of another node (or to find the common ancestor of two nodes) just by applying integer arithmetic.
In fact, sometimes ago I was trying to implement some fancy algorithm that, given two nodes from the open list of a search algorithm, finds their common ancestor. While I was doing this I asked myself if it was possible to use prime numbers in order to provide a labeling system that encodes the “descendant” relation of the nodes.
I think that I have found a theoretical system. Even if it can not be used in real-world applications, I had fun playing with it looking for the properties of the resulting labeled tree. So, I thought it could be interesting to share.