## Which algorithm is best for shortest path?

Table of Contents

What Is the Best Shortest Path Algorithm?

- Dijkstra’s Algorithm. Dijkstra’s Algorithm stands out from the rest due to its ability to find the shortest path from one node to every other node within the same graph data structure.
- Bellman-Ford Algorithm.
- Floyd-Warshall Algorithm.
- Johnson’s Algorithm.
- Final Note.

### How many shortest path algorithms are there?

two

There are two main types of shortest path algorithms, single-source and all-pairs.

**What do you mean by shortest path algorithm?**

The shortest path algorithm is given a weighted graph or digraph G = (V,E,W) and two specified vertices v and w; the algorithm finds a shortest path from v to w. The distance from a vertex v to a vertex w (denoted d(v,w)) is the weight of a shortest path from v to w.

**Does A * guarantee shortest path?**

A* is guaranteed to find the shortest path if the conditions are met (i.e. if you are using an admissible heuristic).

## Is Bellman-Ford algorithm greedy?

Dijkstra’s algorithm is a greedy algorithm that selects the nearest vertex that has not been processed. Bellman-Ford, on the other hand, relaxes all of the edges. and that set of edges is relaxed exactly ∣ V ∣ − 1 |V| – 1 ∣V∣−1 times, where ∣ V ∣ |V| ∣V∣ is the number of vertices in the graph.

### Is a * faster than Dijkstra?

Even though Dijkstra’s algorithm and the A* algorithm both find the same shortest paths, the A* algorithm does it almost 60 times faster!

**Is Dijkstra’s algorithm the best?**

In addition, Best First Search is not optimal [not guaranteed to find the shortest path], and also A*, if you do not use an admissible heuristic function, while Dijkstra’s algorithm is always optimal, since it does not relay on any heuristic.

**Why is the shortest path important?**

Finding the shortest path (SP) in a large-scale network analysis between any two nodes is a tough but very significant task. The SP can help us to analyze the information spreading performance and research the latent relationship in the weighted social network, and so on.

## Can a shortest path contains a cycle?

Shortest paths cannot contain cycles. We already ruled out negative-weight cycles. If there is a positive-weight cycle we can get a shorter path by omitting the cycle, so it can’t be a shortest path with the cycle.

### Is A star greedy?

A* is like Dijkstra’s Algorithm in that it can be used to find a shortest path. A* is like Greedy Best-First-Search in that it can use a heuristic to guide itself.