The heuristic search generally implements on a tree. A tree is a specific case of a sequence of quotient spaces. If in a sequence of hierarchical quotient spaces, the number of elements in each level is finite, then it’s a tree. Assume that SA implements its search on a uniform m-tree. Let be the sub-nodes in the first level. From quotient space point of view, it is equivalent to the partition of domain , where is a set of leaf nodes ...

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