7.3 Kruskal’s Algorithm

1. 7.3 Kruskal’s Algorithm

2. Kruskal’s Algorithm was developed by JOSEPH KRUSKAL

3. Kruskal’s Algorithm • Pick the cheapest link (edge) available and mark it • Pick the next cheapest link available and mark it again • Continue picking and marking link that does not create the circuit ***Kruskal’s algorithm is efficient and optimal

4. Apply Kruskal’s algorithm to find the minimum spanning tree 7 5 4 2 8 10 3 6

5. Apply Kruskal’s algorithm to find the minimum spanning tree 7 5 10 4 2 10 8 3 6 MST: 2+3+4+5+10=24

6. Apply Kruskal’s algorithm to find the minimum spanning tree

7. Apply Kruskal’s algorithm to find the minimum spanning tree

8. Apply Kruskal’s algorithm to find the minimum spanning tree D B H W P

9. This is an isosceles triangle so there must be two equal edges Apply Kruskal’s Algorithm: Since we know that length AB is always longer than the other two edges, so we pick: 212 mi and 212 mi. MST = 424 mi Find the length of the shortest network connecting the three cities A, B, C shown in each figure. C A B 250 mi 300 mi 25° 25° 37° 212 mi A 212 mi B C Apply Kruskal’s Algorithm: Since we know that length AB is always longer than the other two edges, so we pick: 250 mi and 300 mi. MST = 550 mi