Given a B-tree, determine what order the keys were inserted in. There may be multiple answers: I'd like to generate them all.
Is there any known method for this? Or similar problems?
Clarification: As the comments mentioned, enumerating them all may be intractable. I'd like to do two things:
Create a partial ordering. Node 7 was inserted before Node 4, but cannot be compared to Node 20. (I've done this successfully for a binary search tree, and am wondering if this can be applied to B-tree as well. For BSTs, it seems to be simple: Node A < Node B iff Node A is an ancestor of Node B, assuming no deletions.)
Create what I call a probabilistic partial ordering. For example: Out of x possible orderings, y have Node 4 inserted before Node 20, and 1 - y have Node 4 after Node 20. I still am working on this even for binary search trees, so perhaps it's better to ask this question there first.
I'm also working on expanding the model to include deletions (probablisticly), but that will come later.