Minimum Spanning Trees (MSTs)

1
Minimum Spanning Trees (MSTs) Kruskals Algorithm
Basic idea is
Start with a forest of n vertices and no edges
Add edges to the forest in increasing order of
weight
Only add an edge if it joins together two
different sub-trees
2
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
e
d
b
2
4
5
3
2
c
f
3
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
e
d
b
2
4
5
3
2
c
f
4
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
?
3
4
3
1
e
d
b
2
4
5
3
2
c
f
5
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
?
3
4
3
1
e
d
b
2
4
5
3
2
c
f
6
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
?
e
d
b
2
4
5
3
2
c
f
7
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
?
e
d
b
2
4
5
3
2
c
f
8
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
?
3
4
3
1
e
d
b
2
4
5
3
2
c
f
9
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
?
3
4
3
1
e
d
b
2
4
5
3
2
c
f
10
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
?
3
4
3
1
e
d
b
2
4
5
3
2
c
f
11
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
?
3
4
3
1
e
d
b
2
4
5
3
2
c
f
12
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
e
d
b
2
4
5
3
?
2
c
f
13
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
e
d
b
2
4
5
3
?
2
c
f
14
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
e
d
b
2
4
?
5
3
2
c
f
15
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
e
d
b
2
4
?
5
3
2
c
f
16
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
?
e
d
b
2
4
5
3
2
c
f
17
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
4
3
1
?
e
d
b
2
4
5
3
2
c
f
18
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
?
4
3
1
e
d
b
2
4
5
3
2
c
f
19
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
3
?
4
3
1
e
d
b
2
4
5
3
2
c
f
20
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
?
3
4
3
1
e
d
b
2
4
5
3
2
c
f
21
Minimum Spanning Trees (MSTs) Kruskals Algorithm
a
g
?
3
4
3
1
e
d
b
2
4
5
3
2
c
f