Comparing Dijkstra's & Floyd's Algorithms (Edexcel A Level Further Maths: Decision Maths 1)

What is the difference between Dijkstra's and Floyd's algorithms?

• Both algorithms find the shortest path, and its weight (length) between nodes on a graph
• Dijkstra's algorithm finds the shortest path between a fixed starting node and every other node in the network
  • This would be useful where a starting point cannot be moved
    • e.g.  a power station, a distribution warehouse
  • The advantage of Dijkstra's algorithm are speed
    • the algorithm can be stopped once the desired end node is reached
  • The disadvantage of Dijkstra's algorithm is the limited information it provides (compared to Floyd's)
• Floyd's algorithm finds the shortest path between any pair of start and end nodes
  • This would be useful where a starting point can be anywhere on the network
    • e.g. a robot inspecting a network of pipelines
  • The advantage of Floyd's algorithm is the amount of information it provides (compared to Dijkstra)
  • The disadvantage of Floyd's algorithm is the time it takes (especially manually without a computer!)
• Repeating Dijkstra's algorithm, taking each node in turn as the starting node, would produce the same information as Floyd's algorithm