Admissible Heuristics in Pathfinding Algorithms

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What is the purpose of the evaluation function $f(n)$ in the A* search algorithm?

To estimate the total cost of the path from the start node to the goal node through node $n$ (correct)
To calculate the cost of reaching node $n$ from the start node
To determine the order in which nodes are expanded during the search
To estimate the cost of reaching the goal node from node $n$

Which property of the heuristic function $h(n)$ is required for the A* search algorithm to be complete and optimal?

The heuristic function must be monotonic
The heuristic function must be efficient
The heuristic function must be admissible (correct)
The heuristic function must be consistent

What is the main difference between the Uniform Cost Search (UCS) and the A* search algorithm?

UCS expands nodes in order of their depth, while A* expands nodes in order of their breadth
UCS is complete and optimal, while A* is only complete
UCS uses $f(n) = g(n)$, while A* uses $f(n) = g(n) + h(n)$ (correct)
UCS is more efficient than A* for solving problems with uniform cost

Suppose you are using the A* search algorithm to find the shortest path between two cities. Which of the following properties of the heuristic function $h(n)$ would be most desirable?

The heuristic function should be admissible and never underestimate the actual cost to the goal (B) Signup and view all the answers

How does the A* search algorithm expand the search tree compared to other uninformed search methods, such as Breadth-First Search (BFS) or Depth-First Search (DFS)?

A* expands nodes based on their estimated total cost to the goal, while BFS and DFS expand nodes based on their depth or order of discovery (C) Signup and view all the answers

Which of the following statements about the search tree explored by the A* algorithm is true?

The search tree explored by A* is not necessarily a subset of the search tree explored by any other uninformed search method (D) Signup and view all the answers

What is the evaluation function, f, for node F?

11 (D) Signup and view all the answers

Which of the following best defines an admissible heuristic?

Never overestimates the cost to reach the goal state (A) Signup and view all the answers

In the 8-puzzle problem, what does h2(n) represent as a heuristic?

Total Manhattan distance (A) Signup and view all the answers

Which theorem states that if h(n) is admissible, A* using TREE-SEARCH is optimal?

Admissibility theorem (A) Signup and view all the answers

Why is an admissible heuristic important in A* search algorithm?

To guarantee the algorithm finds the optimal solution (C) Signup and view all the answers

What does it mean for an evaluation function to be complete in search algorithms?

It guarantees a solution if one exists (D) Signup and view all the answers

What is the branching factor (b) in the context of search algorithms?

The number of nodes expanded at each level (B) Signup and view all the answers

Which type of search method does Depth Limited Search (DLS) fall under?

Uninformed search - Depth First Search (DFS) (D) Signup and view all the answers

In the context of search algorithms, what does an admissible heuristic mean?

A heuristic that underestimates the cost to reach the goal (C) Signup and view all the answers

What is the purpose of the evaluation function in A* search algorithm?

To calculate the f(n) value for each node (D) Signup and view all the answers

Which search algorithm is known for using a combination of g(n) and h(n) functions for node evaluation?

A* search (A) Signup and view all the answers

In the context of A* search, what does the letter 'A' stand for?

Algorithm (D) Signup and view all the answers