MullOverThings

Useful tips for everyday

# What makes A search optimal?

## What makes A search optimal?

A search algorithm is optimal if no other search algorithm uses less time or space or expands fewer nodes, both with a guarantee of solution quality. The optimal search algorithm would be one that picks the correct node at each choice.

## Which search algorithm is optimal in its search?

Answer: If a search algorithm is optimal, then when it finds a solution it finds the best solution. What are the advantages of breadth-first search (BFS) over depth-first search (DFS)? Answer: BFS is complete and optimal, while DFS is not guaranteed to halt when there are loops.

## Is A * An optimal searching technique?

A* search is optimal only when for all nodes, the forward cost for a node h(x) underestimates the actual cost h*(x) to reach the goal. This property of A* heuristic is called admissibility.

## WHAT IS A* search technique?

A* (pronounced “A-star”) is a graph traversal and path search algorithm, which is often used in many fields of computer science due to its completeness, optimality, and optimal efficiency. One major practical drawback is its. space complexity, as it stores all generated nodes in memory.

## What is A* search explain various stages of A* search with an example?

Here A* Search Algorithm comes to the rescue. What A* Search Algorithm does is that at each step it picks the node according to a value-‘f’ which is a parameter equal to the sum of two other parameters – ‘g’ and ‘h’. At each step it picks the node/cell having the lowest ‘f’, and process that node/cell.

## What is advantage of A * graph search over A * tree search?

The advantage of graph search obviously is that, if we finish the search of a node, we will never search it again. On the other hand, the tree search can visit the same node multiple times. The disadvantage of graph search is that it uses more memory (which we may or may not have) than tree search.

## WHAT IS A * search in AI?

A* is an informed search algorithm, or a best-first search, meaning that it is formulated in terms of weighted graphs: starting from a specific starting node of a graph, it aims to find a path to the given goal node having the smallest cost (least distance travelled, shortest time, etc.).

## Why does the a * search heuristic always find the optimal solution?

A* search finds optimal solution to problems as long as the heuristic is admissible which means it never overestimates the cost of the path to the from any given node (and consistent but let us focus on being admissible at the moment). But why does it always find the optimal solution if the heuristic underestimates?

## Do you need proof that the a * algorithm is optimal?

To clarify, I want a proof that the path found by A* is correct (i.e., is the cheapest/shortest path to the destination), not a proof that the A* algorithm is optimal (i.e., that any other algorithm that uses the same heuristic will expand at least as many nodes as A*).

## Is there a proof of correctness for the a star algorithm?

I’ve been looking for the proof of correctness for the A star (A*) algorithm but none of the texts and websites offer it. Mostly they are talking about the proof of optimality of the A* algorithm. I’m looking for a proof that if the heuristic is admissible, A* will always give an optimal path.

## What’s the difference between a * and best-first search?

The important difference between A* and Best-First search is that A* combines the value given by the estimate function e with the length of the (shortest currently known) path to the node under consideration.