Iterative Deepening Depth-First Search (IDDFS)

Imagine you’re searching for something in a huge maze. You could dive deep down one path using Depth First Search (DFS), but what if that path is incredibly long or even infinite, and the thing you’re looking for is actually close to the start? You might get lost! Alternatively, you could explore level by level using Breadth-First Search (BFS), which guarantees finding the closest item first, but requires remembering every location at the current level, potentially needing a lot of memory.

Iterative Deepening Depth-First Search (IDDFS) is a clever search strategy that tries to get the best of both worlds. It combines the depth-first exploration approach with a level-by-level boundary, making it memory-efficient like DFS while ensuring you find the shallowest solution like BFS.

How IDDFS Works: Combining Depth and Breadth

IDDFS performs multiple DFS searches, but each search has a strict depth limit. It starts with a very shallow limit and gradually increases it in each iteration.

Think of it like this:

1. First Pass (Depth Limit 0): You only check the starting point (like checking only the lobby of the building).
2. Second Pass (Depth Limit 1): You restart the search from the beginning but now explore one step away from the start (like checking the lobby and all rooms directly connected to it on the same floor).
3. Third Pass (Depth Limit 2): You restart again, exploring up to two steps away from the start (checking the lobby, connected rooms, and rooms connected to those rooms, but only up to two steps deep).
4. And so on… You keep restarting the search and increasing the depth limit by one each time (depth_limit = 3, depth_limit = 4, etc.) until you find what you’re looking for.

Because it increases the depth step-by-step, the first time it finds the target, it’s guaranteed to be at the shallowest possible depth, just like BFS. However, because each individual search is a depth-limited DFS, it only needs to keep track of the current path, making it much more memory-efficient than BFS, especially for wide search trees.

The IDDFS Algorithm Steps

The process for IDDFS is quite straightforward:

1. Start with Depth Limit 0: Set the maximum allowed depth (max_depth) to 0.
2. Loop: Start a loop that continues indefinitely (or until the goal is found). a. Perform Depth-Limited Search (DLS): Run a DFS starting from the initial node, but do not explore any nodes beyond the current max_depth. b. Check for Goal: If the DLS finds the target node within the current max_depth, stop the loop and return the result (the goal node or the path to it). c. Increase Depth Limit: If the DLS completes without finding the target node, increment the max_depth by 1. d. Repeat: Go back to step 2a to perform another DLS with the new, larger max_depth.

This iterative process ensures that if a target exists, IDDFS will eventually reach it, and the first time it finds it, it will be via a path with the minimum number of edges (just like BFS).

Example

Advantages and Disadvantages

IDDFS offers a unique blend of features, but it’s not always the perfect choice.

• Advantages:

  • Finds Shortest Path: Like BFS, it guarantees finding the shallowest goal node in an unweighted graph.
  • Memory Efficient: Its memory needs are similar to DFS, typically O(d), where d is the depth of the solution. This is significantly better than BFS’s potentially exponential memory requirement (O(b^d), where b is the branching factor).
  • Complete: Like BFS, it will find a solution if one exists (assuming the graph isn’t infinitely deep).

• Disadvantages:

  • Repeated Work: The biggest drawback is that nodes, especially those near the start node, are visited multiple times in successive iterations. For example, the nodes at depth 1 are visited in the iteration with max_depth = 1, again when max_depth = 2, again when max_depth = 3, and so on.
  • Time Complexity: While the overall time complexity is often the same asymptotically as BFS (O(b^d)), the constant factor can be higher due to the repeated visits in earlier iterations.

When to Use IDDFS

IDDFS shines in specific scenarios:

• Unknown Solution Depth: When you’re exploring a very large (or even infinite) graph or state space and you don’t know how “deep” the solution might be.
• Memory Constraints: When the graph is too large and wide for BFS to fit in memory.
• Shortest Path Needed: When finding the optimal path (in terms of number of steps) is crucial, and a standard DFS might find a suboptimal, deeper solution first.
• Examples: It’s commonly used in artificial intelligence for puzzle solving (like the 15-puzzle) and in game-playing programs where the search tree can be vast.

IDDFS provides a robust way to explore graphs when you need the best of both DFS and BFS, managing the trade-off between computation time and memory usage effectively.

What’s Next?

Explore more advanced DFS techniques and related concepts:

• DFS with Pruning: Learn how to optimize DFS by intelligently skipping branches of the search tree that won’t lead to a solution.
• Bidirectional DFS: Discover a technique that searches from both the start and end nodes simultaneously to potentially find a path faster.
• DFS Time and Space Complexity: Revisit the performance analysis of the basic DFS algorithm to better understand its efficiency.
• How DFS Works: Refresh your understanding of the fundamental steps involved in a standard Depth First Search traversal.