Admissible Heuristics in Pathfinding Algorithms
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Questions and Answers

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?

    <p>The heuristic function should be admissible and never underestimate the actual cost to the goal</p> 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)?

    <p>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</p> Signup and view all the answers

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

    <p>The search tree explored by A* is not necessarily a subset of the search tree explored by any other uninformed search method</p> Signup and view all the answers

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

    <p>11</p> Signup and view all the answers

    Which of the following best defines an admissible heuristic?

    <p>Never overestimates the cost to reach the goal state</p> Signup and view all the answers

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

    <p>Total Manhattan distance</p> Signup and view all the answers

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

    <p>Admissibility theorem</p> Signup and view all the answers

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

    <p>To guarantee the algorithm finds the optimal solution</p> Signup and view all the answers

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

    <p>It guarantees a solution if one exists</p> Signup and view all the answers

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

    <p>The number of nodes expanded at each level</p> Signup and view all the answers

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

    <p>Uninformed search - Depth First Search (DFS)</p> Signup and view all the answers

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

    <p>A heuristic that underestimates the cost to reach the goal</p> Signup and view all the answers

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

    <p>To calculate the f(n) value for each node</p> 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?

    <p>A* search</p> Signup and view all the answers

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

    <p>Algorithm</p> Signup and view all the answers

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