1. Minimum Spanning tree Select any vertex
Prim’s algorithm
Select any vertex
Select the shortest edge connected to that vertex
Select the shortest edge which connects a previously chosen vertex to a new vertex
Repeat step 3 until all vertices have been connected

2. Example
A cable company want to connect five villages to their network which currently extends to the market town of Avenford. What is the minimum length of cable needed? 5
Brinleigh
Cornwell 3 4 6 8 8
Avenford
Donster
Fingley 7 5 4 2
Edan

3. Prim’s algorithm in tabular form
First put the information from the network into a distance matrix A B C D E F - 3 4 7 5 8 6 2

4. A B C D E F - 3 4 7 5 8 6 2 1 3 Brinleigh Avenford
Start at vertex A. Label column A “1” .
Delete row A
Select the smallest entry in column A (AB, length 3) A B C D E F - 3 4 7 5 8 6 2
Avenford
Brinleigh 3

5. A B C D E F - 3 4 7 5 8 6 2 1 2 3 4 Brinleigh Avenford Edan
Label column B “2”
Delete row B
Select the smallest uncovered entry in either column A or column B (AE, length 4) A B C D E F - 3 4 7 5 8 6 2
Avenford
Brinleigh 3
Edan 4

6. A B C D E F - 3 4 7 5 8 6 2 1 2 3 3 4 2 Brinleigh Avenford Donster
Label column E “3”
Delete row E
Select the smallest uncovered entry in either column A, B or E (ED, length 2) A B C D E F - 3 4 7 5 8 6 2
Avenford
Brinleigh 3
Edan 4
Donster 2

7. A B C D E F - 3 4 7 5 8 6 2 1 2 4 3 4 3 4 2 Cornwell Brinleigh
Label column D “4”
Delete row D
Select the smallest uncovered entry in either column A, B, D or E (DC, length 4)
Cornwell 4
Avenford
Brinleigh 3
Edan 4
Donster 2

8. A B C D E F - 3 4 7 5 8 6 2 1 2 5 4 3 4 3 5 4 2 Cornwell Brinleigh
Label column C “5”
Delete row C
Select the smallest uncovered entry in either column A, B, D, E or C (EF, length 5)
Cornwell 4
Avenford
Brinleigh 3
Fingley 5
Edan 4
Donster 2

9. A B C D E F - 3 4 7 5 8 6 2 1 2 5 4 3 6 4 3 5 4 2 Cornwell Brinleigh
FINALLY
Label column F “6”
Delete row F
Cornwell 4
Avenford
Brinleigh 3
Fingley 5
Edan 4
Donster 2

10. A B C D E F - 3 4 7 5 8 6 2 1 2 5 4 3 6 4 3 5 4 2 Cornwell Brinleigh
FINALLY
Label column F “6”
Delete row F
Cornwell 4
Avenford
Brinleigh 3
Fingley 5
Edan 4
Donster 2
The spanning tree is shown in the diagram
Length = 18Km