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Bellman-Ford algorithm

Bellman-Ford algorithm computes single-source shortest paths in a weighted graph (where some of the edge weights may be negative). Dijkstra's algorithm accomplishes the same problem with a lower running time, but requires edges to be non-negative. Thus, Bellman-Ford is usually used only when there are negative edge weights.

Bellman Ford runs in O(VE) time, where V and E are the number of vertices and edges.

Here is a sample algorithm of Bellman-Ford

BF(G,w,s) // G = Graph, w = weight, s=source
Determine Single Source(G,s);
set Distance(s) = 0; Predecessor(s) = nil;
for each vertex v in G other than s, 
   set Distance(v) = infinity, Predecessor(v) = nil;
for i <- 1 to |V(G)| - 1 do   //|V(G)| Number of vertices in the graph
   for each edge (u,v) in G do
      if Distance(v) > Distance(u) + w(u,v) then
         set Distance(v) = Distance(u) + w(u,v), Predecessor(v) = u;  
for each edge (u,r) in G do
   if Distance(r) > Distance(u) + w(u,r);
      return false;
return true;

Proof of the Algorithm

See also:
List of algorithms