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If the branching factor is large, the breadth-first search “OPEN list” may run out of memory. But if the number of states is so large, the statespace graph probably cannot be drawn or represented in memory. So is it not the case that all forms of search will fail?
Not necessarily – it could be that the state being searched for will be located at a fairly shallow position in the tree (thus being found before memory is exhausted), or (if the tree isn’t too deep), you could use depth-first search instead. Also, pruning techniques might help you reduce the effective branching factor by revealing that some paths don’t need to be followed.