# Questions tagged [a-star-search]

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### A* (A-star) search algorithm including closest distance from a node to an obstacle in heuristic and step cost

I want to include the distance of a node to the closest obstacle in the cost function, so that the path length is not only minimal, but also not near obstacles. We know that: Dijkstra's algorithm uses ...
1 vote
80 views

### Simplified Memory Bounded A*

I have been studying the SMA* algorithm and I am having trouble understanding the backup operation. Specifically, I don't understand why the f value of a child node should be the maximum of its own f ...
119 views

### How to avoid costly square root operations in A* algorithm?

As a reminder, in an A* algorithm, vertices in the priority queue are sorted according to their priority $f = g + h$, where $g$ is the cost of getting to this vertex from the start vertex, and $h$ is ...
• 737
1 vote
93 views

### Optimality of A* algorithm

In the book Artificial Intelligence a Modern Approach 4th edition, the author claims that the A* algorithm is cost-optimal if the heuristic function is ...
• 111
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### How is this "pathmax modification," $f(n^\prime) = \max(g(n^\prime) + h(n^\prime), f(n))$, useful?

I am studying the concept of heuristics in search algorithms, and the $A^*$ search algorithm in particular. I am told the following: Greedy search minimises estimated path-cost to goal. But it's ...
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1 vote
115 views

### A* pseudocode problem

What is the difference between this two pseudocode and which one should i implement? ...
222 views

### Any-goal bidirectional A* pathfinding reference

I want to solve the problem of finding a shortest path on a directed weighted graph from a certain node to any of a specified set of destination nodes (preferably the closest one, but that's not that ...
• 121
571 views

### Difference between cost and the heuristic function in A* search

Looking at the image above, thinking in terms of A* search. I don't fully understand the heuristic function. The cost makes sense, so thinking in terms of a traditional map or navigation scenario. I'd ...
106 views

### A* (A-star) path finding in continuous environments with "sticky slower" areas

I have a search problem, finding the shortest path for 3 vehicles to their parking spots, in a continuous environment (inputs are continuous for velocity, turn speed) and the location is continuous, ...
• 207
113 views

### D* Lite - can edge costs be asymmetric?

I'm trying to modify the original D* Lite algorithm adding a margin constraint wrt to any nearby obstacle to be satisfied for each selected cell in the path. This causes the edge cost function between ...
• 145
1 vote
331 views

### Should your heuristic for an A* search algorithm be the same scale as your actual weights?

I'm a bit confused about the scale of heuristics for implementing A* search. $f(n)$ is the total cost of travelling to a node $n$. It is calculated by $f(n) = g(n) + h(n)$. $g(n)$ is the cost of the ...
295 views

### Using A* path finding is giving me inaccurate results

So I am using A* pathfinding to find a path from a person, to a node on a graph. This person has a few 'must pass' nodes that they must go through. So my solution was to run the algorithm for each of ...
301 views

### Are there graphs for which A* cannot be admissible?

Wikipedia states that "On infinite graphs with a finite branching factor and edge costs that are bounded away from zero $(d(x,y)>\varepsilon >0$ for some fixed $\varepsilon$), A* is guaranteed ...
46 views

### Finding multiple paths through a grid such that every grid square is equally used

Setup Here’s the setup: I have an $N$ x $N$ grid of tiles, and a list of $M$ agents that need to move across the grid. Each agent has its own start tile $S(a)$, end tile $E(a)$, and an exact number ...
107 views

### Why doesn't A* give the optimal path for navigating from A to R in this state space?

Well, I have heard that the A* algorithm is optimal and complete. However, when trying to navigate from A to R using A*, it outputs the path, A --> E --> R, although there is a shorter path, A --> M --...
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5k views

### Comparing classical tree-search algorithms (BFS,DFS,A*,IDS) - when to use one or the other?

I have a question about classical tree-search algorithms as I will have an exam soon and this is the type of questions they might be asking. Although I know how to compare the complexities, optimality,...
• 401
994 views

### Coefficients in cost function in A-star

I'd like to expand on this question : https://stackoverflow.com/questions/52420788/why-does-the-a-star-algorithm-need-gn Dijkstra's algorithm uses cost function $f(n) = g(n)$ whereas A* uses cost ...
• 737
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### Can Dijkstra's algorithm outperform A star, in terms of vertices checked?

I know Dijkstra's algorithm can be seen as a specific case of A star, when the estimation heuristic used simply returns 0, so I know that A star with this specific heuristic can not check more ...
• 737
2k views

### A* without heuristic more efficient than Dijkstra

I am using the module networkx to operate on graphs made from OpenStreetMap. I wanted to compare the shortest path algorithm to ...
• 21
87 views

### cheap multi agent path planning algorithms

I am trying to make a tower defence game where some critters are trying to make their ways through a 2D grid-like obstacle course. The idea is these critters cannot walk into the obstacles or into ...
• 123
75 views

### Heuristic for searching for solutions on an 8-puzzle variant with non-unique tiles

I'm trying to perform an A* search on a particular N-puzzle variant in which some tiles are identical. More specifically, assuming an $m \times m$ grid, there are m colors with m tiles of each. The ...
• 151
719 views

### How can an A* algorithm visit all nodes?

Is it possible to find the shortest path and visit all the nodes in a graph by A* algorithm? If yes, how?
57 views

### Term for an A*-like pathfinding strategy where only the heuristic goal distance matters

I am trying to find a proper term for the A*-like best-first pathfinding strategy where the node to expand next is the one with the least estimated distance from the goal, regardless of its distance ...
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If we are given an A$^*$ path search with some heuristic $h$ that yields an optimal path, without knowing that the heuristic is admissible beforehand, would this imply that $h$ is admissible?