Ensuring a Relevant Visiting Order of the Leaf Nodes during a Tree Search

We deene a model for heuristic tree search which assumes that the quality of the heuristic used for ordering the successors of a node improves as depth increases. We show that a usual value ordering heuristic for solving constraint satisfaction problems ts to this model. Our model deenes a partial order on the leaf nodes of the search tree, according to their probability to be a solution. We check which search strategies among interleaved depth-rst search (IDFS), limited discrepancy search (LDS) and depth-bounded discrepancy search (DDS) visit the leaf nodes while respecting the partial order. Our study leads to conclude that, among these strategies, only Pure IDFS and a slight modii-cation of improved LDS respect it.