All - Pairs Shortest Paths ÆÆÆ

In the previous chapter, we saw algorithms to find the shortest path from a source vertex s to a target vertex t in a directed graph. As it turns out, the best algorithms for this problem actually find the shortest path from s to every possible target (or from every possible source to t) by constructing a shortest path tree. The shortest path tree specifies two pieces of information for each node v in the graph: • dist(v) is the length of the shortest path (if any) from s to v;