The best shortest path algorithm

Question

What is the difference between the "Floyd-Warshall algorithm" and "Dijkstra's Algorithm", and which is the best for finding the shortest path in a graph?

I need to calculate the shortest path between all the pairs in a net and save the results to an array as follows:

**A     B     C     D      E** A 0     10    15    5     20 B 10     0    5     5     10 C 15     5    0     10    15 D 5      5    10    0     15 E 20     10    15   15    0 

Answer 1

Dijkstra's algorithm finds the shortest path between a node and every other node in the graph. You'd run it once for every node. Weights must be non-negative, so if necessary you have to normalise the values in the graph first.

Floyd-Warshall calculates the shortest routes between all pairs of nodes in a single run! Cycle weights must be non-negative, and the graph must be directed (your diagram is not).

Johnson's algorithm is using Dijkstra's algorithm to find all pairs in a single pass, and is faster for sparse trees (see the link for analysis).