the part I'm referring to is just about shortest path problems, apparently there is a difference between them but I'm not sure what it could bejim mcnamara said:Hmm. If it computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph I have seen it called both - Bellman-Ford, Bellman.
Bellman did other things for which he was noted. And I know next to nothing about them.
So what is your chapter on about?
Bellman's algorithm, also known as Bellman-Ford algorithm, is a graph traversal algorithm used to find the shortest path from a starting node to all other nodes in a weighted graph. It works by relaxing the edges of the graph in a specific order, gradually improving the estimated distance from the starting node to each node until the optimal path is found.
The time complexity of the Bellman-Ford algorithm is O(V * E), where V is the number of vertices and E is the number of edges in the graph. This means that the algorithm will take longer to run on graphs with a large number of vertices and edges.
Both Bellman's and Dijkstra's algorithms are used to find the shortest path in a weighted graph. However, Dijkstra's algorithm can only be used on graphs with non-negative edge weights, while Bellman's algorithm can handle negative edge weights. Additionally, Dijkstra's algorithm is more efficient than Bellman's algorithm, with a time complexity of O(E + VlogV).
No, Bellman's algorithm cannot be used on graphs with negative cycles. This is because the algorithm relies on relaxing the edges in a specific order, but in a graph with a negative cycle, the shortest path may not exist as the algorithm can get stuck in an infinite loop.
The shortest path is calculated by keeping track of the distance from the starting node to each node in the graph. The algorithm then iterates through all the edges in the graph, relaxing them in a specific order until the optimal distance to each node is found. The path can then be traced back from the end node to the starting node using the parent nodes that were updated during the relaxation process.