Bellman-Ford algorithm

At which point the normal Bellman-Ford algorithm is used to recover a new route.

Bellman-Ford algorithm solves the single-source problem if edge weights may be negative.

The main disadvantages of the Bellman-Ford algorithm in this setting are as follows:

Distance vector algorithms use the Bellman-Ford algorithm.

Distance-vector routing protocols use the Bellman-Ford algorithm.

This method allows the Bellman-Ford algorithm to be applied to a wider class of inputs than Dijkstra.

Distance-vector routing protocols are based on a distributed form of Bellman-Ford algorithm to find shortest paths.

WRP uses an enhanced version of the distance-vector routing protocol, which uses the Bellman-Ford algorithm to calculate paths.

WRP, similar to DSDV, inherits the properties of the distributed Bellman-Ford algorithm.

With Richard Bellman, Ford also developed the Bellman-Ford algorithm for finding shortest paths in graphs that have negatively weighted edges.

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.

The basic idea of SPFA is the same as Bellman-Ford algorithm in that each vertex is used as a candidate to relax its adjacent vertices.

Hence, one can easily formulate the solution for finding shortest paths in a recursive manner, which is what the Bellman-Ford algorithm or the Floyd-Warshall algorithm does.

Compute dist(u), the shortest path distance from root v to vertex u in G using Dijkstra's algorithm or Bellman-Ford algorithm.

A distributed variant of the Bellman-Ford algorithm is used in distance-vector routing protocols, for example the Routing Information Protocol (RIP).

It works by using the Bellman-Ford algorithm to compute a transformation of the input graph that removes all negative weights, allowing Dijkstra's algorithm to be used on the transformed graph.

The Bellman-Ford algorithm sometimes referred to as the Label Correcting Algorithm, computes single-source shortest paths in a weighted digraph (where some of the edge weights may be negative).

In such a case, the Bellman-Ford algorithm can detect negative cycles and report their existence, but it cannot produce a correct "shortest path" answer if a negative cycle is reachable from the source.

Destination-Sequenced Distance-Vector Routing (DSDV) is a table-driven routing scheme for ad hoc mobile networks based on the Bellman-Ford algorithm.

The Shortest Path Faster Algorithm (SPFA) is an improvement of the Bellman-Ford algorithm which computes single-source shortest paths in a weighted directed graph.

This is similar to a situation which arises in graph algorithms: the Bellman-Ford algorithm and Floyd-Warshall algorithm appear to have the same running time () if only the number of vertices is considered.

If the Bellman-Ford algorithm is used, the running time becomes , or the edge cost can be shifted with a potential to achieve running time with the Dijkstra algorithm and Fibonacci heap.

In contrast, for arbitrary graphs the shortest path may require slower algorithms such as Dijkstra's algorithm or the Bellman-Ford algorithm, and longest paths in arbitrary graphs are NP-hard to find.

However, since it terminates upon finding a negative cycle, the Bellman-Ford algorithm can be used for applications in which this is the target to be sought - for example in cycle-cancelling techniques in network flow analysis.

However, a more precise analysis which accounts for the number of edges as a separate parameter assigns the Bellman-Ford algorithm a time of , which is only quadratic in the size of the input (rather than cubic).