disjoint pattern databases

Disjoint pattern databases are used in heuristic functions to solve problems such as the 15-puzzle. What I don't understand is how the groups are considered disjoint? As in, if you select a subproblem of the problem (such as tiles 1, 2, 3, and 4), your moves will have to affect the tiles around those tiles as you try to get them to their goal state. Therefore, you cannot just add up the subproblems as it will not be an admissible heuristic function.

Is it because the database does not count when other tiles are moved that are not in the pa开发者_如何学JAVArticular subproblem?

Yes, as per the disjoint pattern databases paper, you are right. They say this is the key difference between "non-additive" databases and disjoint databases.