Example A cable company want to connect five villages to their network which currently extends to the market town of Avonford. What is the minimum.

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Presentation transcript:

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

We model the situation as a network, then the problem is to find the minimum connector for the network A F B C D E 2 7 4 5 8 6 3

Kruskal’s Algorithm B C 3 6 8 A D F 7 5 4 2 E List the edges in order of size: ED 2 AB 3 AE 4 CD 4 BC 5 EF 5 CF 6 AF 7 BF 8 DF 8 A F B C D E 2 7 4 5 8 6 3

Kruskal’s Algorithm Select the shortest edge in the network B C 3 6 8 F B C D E 2 7 4 5 8 6 3

Kruskal’s Algorithm B C 3 6 8 A D F 7 5 4 2 E Select the next shortest edge which does not create a cycle ED 2 AB 3 A F B C D E 2 7 4 5 8 6 3

Kruskal’s Algorithm B C 3 6 8 A D F 7 5 4 2 E Select the next shortest edge which does not create a cycle ED 2 AB 3 CD 4 (or AE 4) A F B C D E 2 7 4 5 8 6 3

Kruskal’s Algorithm B C 3 6 8 A D F 7 5 4 2 E Select the next shortest edge which does not create a cycle ED 2 AB 3 CD 4 AE 4 A F B C D E 2 7 4 5 8 6 3

Kruskal’s Algorithm B C 3 6 8 A D F 7 5 4 2 E Select the next shortest edge which does not create a cycle ED 2 AB 3 CD 4 AE 4 BC 5 – forms a cycle EF 5 A F B C D E 2 7 4 5 8 6 3

Kruskal’s Algorithm B C 3 6 8 A D F 7 5 4 2 E All vertices have been connected. The solution is ED 2 AB 3 CD 4 AE 4 EF 5 Total weight of tree: 18 A F B C D E 2 7 4 5 8 6 3