# 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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### Doesn't an admissible heuristic ensure optimality in the graph-search version of A*?

I'm reading a text book "Artificial Intelligence - A Modern Approach (3rd Edition)". In page 95, the book mentions that "A* has the following properties: the tree-search version of A* ...
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### How do we know that $c(n,a,G) = h^{\ast}(n)$, in the proof that if a heuristic is consistent then it is admissible?

I found a proof that if a heuristic $h$ is consistent, then it is admissible, but I'm confused by one of the steps in the proof. The proof is by induction on $k$, the number of actions from a node $n$ ...
97 views

### Which search algorithm expands nodes closest to the goal?

I want to know which search algorithm among A* and Best-First Search and Greedy First Search expands nodes closest to the goal. I have three opinions about A* and Best-First Search and Greedy First ...
127 views

### How do I construct a state space that shows that Greedy Best First Search is not complete while A* is?

Construct a state space with appropriate heuristics and local costs. Show that Greedy Best First search is not complete for the state space. Also illustrate A* is complete and guarantees solution for ...
119 views

### What is a good algorithm (and a heuristic) to find the shortest path in a puzzle game?

In a 3D world, there is a Robot, boxes, and switches. The robot's job is to carry boxes (one box at a time) and put them on top of switches to solve the level. All switches must have a box on top for ...
3k views

### What does consistency of heuristic intuitively mean in the A* algorithm and why are consistent heuristics monotonic?

Could someone give the intuition behind consistency of heuristic function in the A* algorithm? From wikipedia: Every node i will give an estimate that, after accounting for the cost to reach i + 1, ...
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1 vote
127 views

### Is N the total number of nodes in the frontier plus the number of nodes in the explored list?

I'm studying fundamentals of AI from the classic Russell-Norvig book (3rd edition). I have a small doubt about the effective branching factor, which is defined as follows (section 3.6.1, p. 103): One ...
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606 views

### Where can I find Norvig's version of the pseudocode for the A* search algorithm?

Can anybody point me to a link to Peter Norvig's version of the A* pseudocode. I've googled it interminably but found nothing. It's the version that uses the Unexplored/Frontier/Explored data ...
292 views

### Is possible to perform an early goal test with A* using a consistent heuristic?

I have a doubt about A* goal test. As far as I know an early goal test is performed when a node (representing a certain state) is inserted in the frontier or, to conform with AIMA terminology, when is ...
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### Is there an error in A* optimality proof Russel-Norvig 4th edition?

In "AI: A Modern Approach", 4th edition, by Russell and Norvig, they give a purported proof that A* is cost-optimal for any admissible heuristic. The given proof seems most certainly wrong. ...
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### 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 ...
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120 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 ...
1k 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 ...
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### How do we determine whether a heuristic function 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 heuristic functions. Currently, I explored the Manhattan and Euclidean ...
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