Depth limited search algorithm with example
Posted: Wed Aug 16, 2023 12:02 pm
Depth-Limited Search (DLS) is a search algorithm that explores a search tree or graph up to a specified depth limit. It is a variant of depth-first search (DFS) that prevents excessive exploration by limiting the depth of the search. DLS is particularly useful when the search space is large or infinite, and a complete DFS could potentially get stuck in infinite loops.
Here's an example of the Depth-Limited Search algorithm applied to a simple tree structure:
Consider the following tree structure, where each node is labeled with a letter:
Let's say we want to find a path from node 'A' to node 'G' using DLS with a depth limit of 2. Here's how the algorithm would work:
Initialization:
Start at the initial node 'A'.
Set the depth limit to 2.
Depth-Limited Search:
Explore node 'A' at depth 0. Since the depth limit is 2, we can expand its children ('B' and 'C') at depth 1.
Depth 1:
Expand node 'B'. Its children ('D', 'E', 'F') are at depth 2, which is within the limit.
Expand node 'C'. Its child 'G' is also at depth 2.
Depth 2:
Expand node 'D'. No more children to expand at depth 2.
Expand node 'E'. No more children to expand at depth 2.
Expand node 'F'. No more children to expand at depth 2.
Expand node 'G'. No more children to expand at depth 2.
Goal Check:
At depth 2, we have explored all nodes. We found the goal node 'G' at depth 2.
Path Reconstruction:
Reconstruct the path from the initial node 'A' to the goal node 'G': A -> C -> G.
In this example, the Depth-Limited Search algorithm reached the goal node 'G' within the specified depth limit of 2. It explored nodes at depths 0, 1, and 2 while preventing the search from continuing beyond depth 2.
Depth-Limited Search is useful when you want to balance between depth-first exploration and avoiding excessive memory usage or infinite loops. However, it's important to note that DLS might miss solutions that are deeper in the search space if the depth limit is too restrictive. Iterative Deepening Search (IDS) is a technique that can be used to overcome this limitation by gradually increasing the depth limit in successive iterations.
Here's an example of the Depth-Limited Search algorithm applied to a simple tree structure:
Consider the following tree structure, where each node is labeled with a letter:
Code: Select all
A
/ \
B C
/|\ \
D E F G
Initialization:
Start at the initial node 'A'.
Set the depth limit to 2.
Depth-Limited Search:
Explore node 'A' at depth 0. Since the depth limit is 2, we can expand its children ('B' and 'C') at depth 1.
Depth 1:
Expand node 'B'. Its children ('D', 'E', 'F') are at depth 2, which is within the limit.
Expand node 'C'. Its child 'G' is also at depth 2.
Depth 2:
Expand node 'D'. No more children to expand at depth 2.
Expand node 'E'. No more children to expand at depth 2.
Expand node 'F'. No more children to expand at depth 2.
Expand node 'G'. No more children to expand at depth 2.
Goal Check:
At depth 2, we have explored all nodes. We found the goal node 'G' at depth 2.
Path Reconstruction:
Reconstruct the path from the initial node 'A' to the goal node 'G': A -> C -> G.
In this example, the Depth-Limited Search algorithm reached the goal node 'G' within the specified depth limit of 2. It explored nodes at depths 0, 1, and 2 while preventing the search from continuing beyond depth 2.
Depth-Limited Search is useful when you want to balance between depth-first exploration and avoiding excessive memory usage or infinite loops. However, it's important to note that DLS might miss solutions that are deeper in the search space if the depth limit is too restrictive. Iterative Deepening Search (IDS) is a technique that can be used to overcome this limitation by gradually increasing the depth limit in successive iterations.