By combining iterative-deepening with A*, we produce an algorithm that is optimal and complete (like A*) and that has the low memory requirements of depth-first search

IDA* is a form of iterative-deepening search where successive iterations impose a greater limit on f(node) rather than on the depth of a node.

IDA* performs well in problems where the heuristic value f (node) has relatively few possible values.

For example, using the Manhattan distance as a heuristic in solving the eight-queens problem, the value of f (node) can only have values 1, 2, 3, or 4.

In this case, the IDA* algorithm only needs to run through a maximum of four iterations, and it has a time complexity not dissimilar from that of A*, but with a significantly improved space complexity because it is effectively running depth-first search.

In cases such as the traveling salesman problem where the value of f (node) is different for every state, the IDA* method has to expand 1 + 2 + 3 + . . . + n nodes = O(n2) where A* would expand n nodes.