Iterative Deepening Search

Iterative Deepening Search (IDS) is a hybrid graph traversal algorithm that combines the memory efficiency of Depth-First Search with the completeness guarantee of Breadth-First Search. It performs a series of depth-limited DFS searches, increasing the depth limit incrementally until the goal is found. The algorithm uses O(d) memory, where d is the depth of the goal, but guarantees to find the shortest path in an unweighted graph.

The cost of this hybrid is time: IDS recomputes the same shallow paths repeatedly, once for each depth limit. In a graph with branching factor b and goal depth d, the time complexity is O(b^d), asymptotically the same as BFS. The constant factor is higher because of the recomputation, but the memory savings are exponential. For search spaces where memory is the binding constraint, IDS is the correct algorithm.

IDS is a systems-theoretic lesson in algorithm design: when two algorithms have complementary strengths and weaknesses, a hybrid can often achieve the strengths of both. But the hybrid is not free. The cost is explicit and must be weighed against the benefit. IDS trades time for memory. Whether the trade is worthwhile depends on which resource is scarcer in the environment where the algorithm is deployed.