A LIFO (last-in-first-out) stack is used to store the frontier set of which search algorithms

The LIFO (Last-In-First-Out) stack is used to store the frontier set of the Depth-First Search (DFS) algorithm.

Here's a step-by-step explanation:

1. In the Depth-First Search algorithm, we start from the root (or any arbitrary node) and explore as far as possible along each branch before backtracking.

2. A stack (which follows the LIFO principle) is used to remember to get the next vertex to start a search when a dead end occurs in any iteration.

3. We insert the root into the stack to start the algorithm.

4. Then, as long as the stack is not empty, we:

   • Remove the top item from the stack.
   • If the removed item has unvisited vertices, then we select one unvisited vertex, mark it as visited, and push it into the stack.
   • If the removed item doesn’t have any unvisited vertices, then we are done with that item and we remove it from the stack.

5. Repeat step 4 until the stack is empty.

So, the LIFO stack is used to store the frontier set of the Depth-First Search algorithm.