Questions tagged [a-star]
For questions related to the A* (or A) search algorithm.
21
questions
8
votes
1answer
9k views
Why is A* optimal if the heuristic function is admissible?
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 ...
7
votes
3answers
18k 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?
5
votes
1answer
5k 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 ...
5
votes
2answers
350 views
How does A* search work given there are multiple goal states?
When I have read through the fundamentals of AI, I saw a situation (i.e., a search space) which is illustrated in the following picture.
These are the heuristic estimates:
...
5
votes
1answer
199 views
How do we determine whether a heuristic is better than another?
I am trying to solve a Maze puzzle using the A* algorithm. I am trying to analyze the algorithm based on different applicable heuristics.
Currently, I explored the Manhattan and Euclidean distances. ...
5
votes
1answer
113 views
A* is similar to Dijkstra with reduced cost
According to this Wikipedia article
If the heuristic $h$ satisfies the additional condition $h(x) ≤ d(x, y) + h(y)$ for every edge $(x, y)$ of the graph (where $d$ denotes the length of that edge), ...
4
votes
1answer
3k 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?
3
votes
1answer
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.
3
votes
1answer
162 views
A* and uniform-cost search are apparently incomplete
Consider the following diagram of a graph representing a search space.
If we start at $B$ and try to reach goal state $E$, the lowest-cost first search (LCFS) (aka uniform-cost search) algorithm ...
2
votes
1answer
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 $n$?
2
votes
1answer
150 views
Understanding the proof that A* search is optimal
I don't understand the proof that $A^*$ is optimal.
The proof is by contradiction:
Assume $A^*$ returns $p$ but there exists a $p'$ that is cheaper. When $p$ is chosen from the frontier, assume $...
2
votes
1answer
76 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 $p$ ...
2
votes
1answer
345 views
Why Nilsson's Sequence Score isn't an admissible heuristic?
I understand what an admissible heuristic is, I just don't know how to tell whether one heuristic is admissible or not. So, in this case, I'd like to know why Nilsson heuristic isn't admissible.
2
votes
1answer
71 views
2
votes
0answers
34 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 ...
2
votes
0answers
113 views
How can I assign agents to tasks based on time and affinity?
I am working on an assignment problem.
Consider $K$ agents $A_1, \dots A_K$ and $N$ tasks $T_1, \dots T_N$. Each task has a certain time $t(T_i)$ to be completed and each agent has a matching (or ...
2
votes
1answer
70 views
In the graph search version of A*, can I stop the search the first time I encounter the goal node?
I am going through Russel and Norvig's Artificial Intelligence: A Modern Approach (3rd edition). I was reading the part regarding the A* algorithm
A* graph search version is optimal when heuristic ...
1
vote
1answer
81 views
What does a consistent heuristic become if an edge is removed in A*?
For the A* algorithm, a consistent heuristic is defined as follows:
if, for every node $n$ and every successor $m$ of $n$ generated by any action $a$, $h(n) \leq c(n,m) + h(m)$.
Suppose the edge $c(...
1
vote
1answer
35 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 ...
0
votes
2answers
82 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.
0
votes
1answer
63 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 ...
