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 shorte

Answer 1

In the meanwhile better algorithms for the single source shortest path problem are known. A practically relevant one is a derivation of Dijkstra's algorithm by Torben Hagerup. The algorithm has the same worst case complexity as Djikstra's, but in the average case the expected runtime is linear in the size of the graph, which is much faster than the pure Dijkstra. The idea of the algorithm is based on the idea, that there is no need to always poll the minimum edge from the queue. It is possible poll an edge from the queue, whose weight is 1+k times as large as the minimum edge weight, where k is some number larger 0. Even if such an edge is chosen, the algorithm will still find the shortest path.