1. Kruskal’s Algorithm Elaicca Ronna Ordoña

2. 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 4 5 3 8 Example

3. A F B C D E 2 7 4 5 8 6 4 5 3 8

4. The steps are: 1. Sort all the the weight of the edges in ascending order. 2. Pick the smallest edge. Check if it forms a cycle with the spanning tree formed so far. If cycle is not formed, include this edge. Else, discard it. 3. Repeat step#2 until there are (V-1) edges in the spanning tree.

5. A F B C D E 2 7 4 5 8 6 4 5 3 8 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 CF 8 Kruskal’s Algorithm

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

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

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

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

10. 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 Kruskal’s Algorithm A F B C D E 2 7 4 5 8 6 4 5 3 8

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

12. 4 1 2 3 2 1 3 5 3 4 2 56 4 4 10 A BC D E F G H I J Complete Graph

13. 1 4 2 5 2 5 4 3 4 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J AABD BB B CD JC C E F D DH JEG FFGI GGIJ HJJI

14. 2 5 2 5 4 3 4 4 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Sort Edges

15. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Add Edge

16. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Add Edge

17. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Add Edge

18. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Add Edge

19. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Add Edge

20. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Cycle Don’t Add Edge

21. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Add Edge

22. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Add Edge

23. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Add Edge

24. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Cycle Don’t Add Edge

25. 2 5 2 5 4 3 4 4 10 1 6 3 3 2 1 2 3 2 1 3 5 3 4 2 56 4 4 A BC D E F G H I J B B D J C C E F D DH J EG F F G I G G I J HJ JI 1 AD 4 BC 4 AB Add Edge

26. 4 1 2 2 1 3 3 2 4 A BC D E F G H I J 4 1 2 3 2 1 3 5 3 4 2 56 4 4 10 A BC D E F G H I J Minimum Spanning TreeComplete Graph