7.3 Kruskal

1
7.3 Kruskals Algorithm
2

• Kruskals Algorithm was developed by
• JOSEPH KRUSKAL

3
Kruskals 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
• Kruskals algorithm is efficient and optimal

4
Apply Kruskals algorithm to find the minimum
spanning tree
7
5
4
2
8
10
3
6
5
Apply Kruskals algorithm to find the minimum
spanning tree
7
5
4
10
2
8
10
3
6
MST 23451024
6
Apply Kruskals algorithm to find the minimum
spanning tree
7
Apply Kruskals algorithm to find the minimum
spanning tree
8
Apply Kruskals algorithm to find the minimum
spanning tree
D
B
H
W
P
9
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
212 mi
A
B
C

• This is an isosceles triangle so there must be
  two equal edges
• Apply Kruskals 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

Apply Kruskals 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