1. Networks Prim’s Algorithm
Decision Maths
Networks
Prim’s Algorithm

2. Prim`s Algorithm
In Lesson 1 we learnt about Kruskal`s algorithm, which was used to solve minimum connector problems.
Another method that can be used is Prim`s algorithm.
Step 1 – Select any node
Step 2 – Connect it to the nearest node
Step 3 – Connect one node already selected to the nearest unconnected node.
Step 4 – Repeat 3 until all nodes are connected.

3. Prim`s Algorithm Consider the example we looked at last lesson.
Select any node you like.
Lets select F.

4. Prim`s Algorithm Connect it to the nearest node.
C and D are both 3 away so we can choose either.
Lets select C.

5. Prim`s Algorithm
The nearest node to either of F or C is D, which is only 3 away from F.
So connect D to F.

6. Prim`s Algorithm The nearest to D, F or C is E which is 2 from D.
So connect E to D.

7. Prim`s Algorithm
The nearest to any of these four nodes is A which is 5 away from F.
Connect A to F.

8. Prim`s Algorithm We now need to connect the last node, B.
The shortest arc is AB, which is 2.
Connect B to A.

9. Prim`s Algorithm
All the nodes are now connected so this is the minimum connector or minimal spanning tree.

10. Distance Table The Network can also be represented as a table.
The infinity symbol (∞) means there is no edge between the two nodes.

11. Prim`s on a Distance Table
We are going to apply Prim`s algorithm to the distance table.
This demonstrates how a computer could apply the algorithm.
Prim`s is more suitable than Kruskal`s as computers have a problem recognising loops.
As you go through the algorithm, see if you can relate the procedure to the last example.

12. Prim`s on a Distance Table
Step 1 – Select any arbitrary node.
Step 2 – Delete the row and loop the column that correspond to the node selected.
Step 3 – Choose the smallest number in the loop.
Step 4 – Delete the row that this smallest number is in.
Step 5 – Loop the column that corresponds to the row just deleted.
Step 6 – Choose the smallest number in any loop.
Step 7 – Repeat steps 4, 5 and 6 until all rows have been deleted and columns looped.

13. Prim`s on a Distance Table
Here I have chosen F.
Delete the row.
Loop the column.
Select the smallest number in the loop.

14. Prim`s on a Distance Table
Delete row C.
Loop column C.
Select the smallest number in any loop that is not crossed out.

15. Prim`s on a Distance Table
Delete row D.
Loop column D.
Select the smallest number in any loop that is not crossed out.

16. Prim`s on a Distance Table
Delete row E.
Loop column E.
Select the smallest number in any loop that is not crossed out.

17. Prim`s on a Distance Table
Delete row A.
Loop column A.
Select the smallest number in any loop that is not crossed out.

18. Prim`s on a Distance Table
Delete row B.
Loop column B.

19. Prim`s on a Distance Table
The algorithm is complete when all the columns have been looped and the rows crossed out.
The circles show the edges in the minimum connector.

20. Prim`s on a Distance Table
In this case they are AB, DE, AF, CF, DF
Can you explain why this procedure is exactly the same as applying Prim`s algorithm?