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Implement proper id accessors

The current implementation of ids works well only if the root does not change and nodes are attached to nodes that already have the correct root. In order to support all use cases, the id table that the root node maintains needs to be split when a sub-tree is removed.

A couple of ideas:

  1. All parent nodes should maintain a current table of correct ids. When a node with an id is added, it is propagated to the root. When a node is removed, the id is removed from all ancestors.
  2. The id table is built on demand using a graph traversal method to build the entire id table. This would only need to happen when a sub-tree is flagged as dirty when it is removed from another tree that contains the root node.

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