I am just learning how to implement the Nested Set Model but still have confusion with a certain aspect of it involving items that may be part of multiple categories. Given
You do not avoid duplications and the apple (or a reference to the apple) will be placed twice in your tree otherwise it won't be a tree but rather a graph. Your question is equally applicable if you build a... Swing JTree or an HTML tree ;).
The nested set model is just an efficient way to push and traverse a tree structure in a relational DB.It is not a data structure itself. It's more popular among MySQL users since MySQL lacks functionality for processing tree structures (e.g. like the one that Oracle provides).
Cheers!