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Posted November 11, 2021 at 10:04 am
See Part I for an overview of Dijkstra algorithm and Part II for pseudo code of Dijkstra algorithm.
As we have seen, the Dijkstra Algorithm is used to solve the problem of minimum paths in a directed graph. The implementation we have been analysing always gives us the optimal matrix of minimum paths.
Typical applications of the Dijkstra algorithm:
Graphs
| Graph | Vertices | Edges |
| Financial | Stocks, currency | Transactions |
| Neural networks | Neurons | Synapses |
| Scheduling | Tasks | Precedence constraints |
| Communication | Telephones, computers | Fibre optic cables |
| Circuits | Gates, registers, processors | Wires |
| Mechanical | Joints | Rods, beams, springs |
| Hydraulic | Reservoirs, pumping stations | Pipelines |
| Games | Board positions | Legal moves |
| Internet | Web pages | Hyperlinks |
Dijkstra algorithm and Kruskal algorithm – both these algorithms belong to the family of greedy algorithms. Although Dijkstra algorithm is used to solve the shortest path problem, the Kruskal algorithm is used to solve the minimum covering graph.
Dijkstra algorithm and Prim algorithm – both algorithms belong to the family of greedy algorithms. Although the Dijkstra algorithm is used to solve the shortest path problem, the Prim algorithm is used to solve the minimum covering graph as the Kruskal algorithm.
What is the difference between Prim algorithm and Kruskal algorithm? The difference is in the way the greedy algorithm is implemented. While the Kruskal algorithm always chooses the edges in increasing order of length and forms disjoint subsets to finally find the optimal solution, the Prim algorithm always has the optimal set at a given time.
Stay tuned for the next installment in which Mario Pisa will demonstrate how to find the shortest path using the Dijkstra algorithm.
Visit QuantInsti for additional insight on this topic: https://blog.quantinsti.com/dijkstra-algorithm/
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