# Questions tagged [a-star]

For questions related to the A* (or A) search algorithm, which is a very famous state-space search algorithm and widely taught in Computer Science and Artificial Intelligence. A* is a best-first search algorithm that is guaranteed to find the optimal solution given an admissible heuristic function, so A* is also an informed search algorithm, as opposed to e.g. depth-first search, which is an uninformed search algorithm.

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### If $h_1(n)$ is admissible, why does A* tree search with $h_2(n) = 3h_1(n)$ return a path that is at most thrice as long as the optimal path?

Consider a heuristic function $h_2(n) = 3h_1(n)$. Where $h_1(n)$ is admissible. Why are the following statements true? $A^*$ tree search with $h_2(n)$ will return a path that is at most thrice as ...
62 views

### Is there any situation in which breadth-first search is preferable over A*?

Is there any situation in which breadth-first search is preferable over A*?
27 views

### Incorrect node expansion in game board with A* search

I have the following game board below, and we're using A* search to find the optimal path from the agent to the key. There are 8 directions. Up, down, left, right have a cost of 1, and diagonal ...
185 views

### What is the difference between the heuristic function and the evaluation function in A*?

I am reading college notes on state search space. The notes (which are not publicly available) say: To do state-search space, the strategy involves two parts: defining a heuristic function, and ...
37 views

### Why do we use the tree-search version of breadth-first search or A*?

In Artiﬁcial Intelligence A Modern Approach, search algorithms are divided into tree-search version and graph-search version, where the graph-search version keeps an extra explored set to avoid ...
1k views

### What are the differences between Q-Learning and A*?

Q-learning seems to be related to A*. I am wondering if there are (and what are) the differences between them.
231 views

### Is A* with an admissible but inconsistent heuristic optimal?

I understand that, in tree search, an admissible heuristic implies that $A*$ is optimal. The intuitive way I think about this is as follows: Let $P$ and $Q$ be two costs from any respective nodes $p$ ...
99 views

### Which heuristics guarantee the optimality of A*?

The following is a statement and I am trying to figure out if it's true or false and why. Given a non-admissible heuristic function, A* will always give a solution if one exists, but there is no ...
49 views

### Doesn't the number of explored nodes with IDA* increase linearly?

I think I'm misunderstanding the description of IDA* and want to clarify. IDA* works as follows (quoting from Wiki): At each iteration, perform a depth-first search, cutting off a branch when its ...
39 views

### How does heuristic work with multiple agents?

I have a question for heuristic search with multiple agents. I know how heuristic search works with one agent (ex. one Pacman) but I don't really understand it with multiple agents. Let's say we have ...
104 views

156 views

### A* is similar to Dijkstra with reduced cost

According to this Wikipedia article If the heuristic $h$ satisfies the additional condition $h(x) \leq d(x, y) + h(y)$ for every edge $(x, y)$ of the graph (where $d$ denotes the length of that edge),...
153 views

### How can the A* algorithm be optimized?

How can the A* algorithm be optimized? Any references that shows the optimization of A* algorithm are also appreciated.
104 views

### How can I calculate the shortest path between two 2d vector points in an environment with obstacles?

I have a 2D plane, with a fixed height and width of 10M. The plane has an agent (or robot) in the point $(1, 2.2)$, and an electric outlet in the point $(8.2, 9.1)$. The plane has a series of ...
81 views

### What kind of search method is A*?

What kind of search method is A*? Explain to me with an example.
5k views

### How do I show that uniform-cost search is a special case of A*?

How do I show that uniform-cost search is a special case of A*? How do I prove this?
71 views

### How is the cost of the path to each node computed in A*?

How is the cost of the path to each node $n$ computed in the A* algorithm? Do we need to add the cost of the path to the parent node $p$ to the cost of the path of the child node $n$?
27k views

### What are the differences between A* and greedy best-first search?

What are the differences between the A* algorithm and the greedy best-first search algorithm? Which one should I use? Which algorithm is the better one, and why?
7k views

### How is iterative deepening A* better than A*?

The iterative deepening A* search is an algorithm that can find the shortest path between a designated start node and any member of a set of goals. The A* algorithm evaluates nodes by combining the ...
4k views

### What heuristic to use when doing A* search with multiple targets? [closed]

Usually, using the Manhattan distance as a heuristic function is enough when we do an A* search with one target. However, it seems like for multiple goals, this is not the most useful way. Which ...
4k views

### How do you calculate the heuristic value in this specific case?

The A* algorithm uses the "evaluation function" $f(n) = g(n) + h(n)$, where $g(n)$ = cost of the path from the start node to node $n$ $h(n)$ = estimated cost of the cheapest path from $n$ to the ...
A heuristic is admissible if it never overestimates the true cost to reach the goal node from $n$. If a heuristic is consistent, then the heuristic value of $n$ is never greater than the cost of its ...