Bellman-Ford
In one example
by: Juan Rodriguez
Definition
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph[1]
It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers.
| Worst-case performance | |
| Best-case performance | |
| Worst-case space complexity |
{\displaystyle \Theta (|V||E|)}{\displaystyle \Theta (|V||E|)}
{\displaystyle \Theta (|E|)}{\displaystyle \Theta (|E|)}
{\displaystyle \Theta (|V|)}{\displaystyle \Theta (|V|)}
Example
- Set 0 to source node
- At each iteration we need to examine all the edges
- Update distances in the table based on the shortest path from the source node
- Repeat steps if any distance is updated
| 0 | 1 | 2 | 8 | Inf | Inf |
| A | B | C | D | E | F |
1st Iteration
6 vertices = max 5 iterations
| 0 | 1 | 2 | 7 | 4 | 10 |
| A | B | C | D | E | F |
2st Iteration
Example
| 0 | 1 | 2 | 7 | 4 | 8 |
| A | B | C | D | E | F |
3st Iteration
6 vertices = max 5 iterations
| 0 | 1 | 2 | 7 | 4 | 8 |
| A | B | C | D | E | F |
4st Iteration
Example
No changes, finished!
6 vertices = max 5 iterations
References
[1] https://en.wikipedia.org/wiki/Bellman%E2%80%93Ford_algorithm
[2] https://www.geeksforgeeks.org/bellman-ford-algorithm-dp-23/