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CS 3343 Analysis of Algorithms Minimum Spanning Trees – 1
Minimum Spanning Trees
Introduction
Safe Edges
Kruskal’s Algorithm
Prim’s Algorithm
Minimum Spanning Tree Definition
⊲ Definition
Example MST
Safe Edges 1
Safe Edges 2
Safe Edges 3
Safe Edges 4
Kruskal 1
Kruskal 2
Prim 1
Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 2
Minimum Spanning Tree Example
Definition
⊲ Example MST
Safe Edges 1
Safe Edges 2
Safe Edges 3
Safe Edges 4
Kruskal 1
Kruskal 2
Prim 1
Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 3
Safe Edges
Definition
Example MST
⊲ Safe Edges 1
Safe Edges 2
Safe Edges 3
Safe Edges 4
Kruskal 1
Kruskal 2
Prim 1
Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 4
Safe Edge Theorem
Definition
Example MST
Safe Edges 1
⊲ Safe Edges 2
Safe Edges 3
Safe Edges 4
Kruskal 1
Kruskal 2
Prim 1
Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 5
Example of a Cut
Definition
Example MST
Safe Edges 1
Safe Edges 2
⊲ Safe Edges 3
Safe Edges 4
Kruskal 1
Kruskal 2
Prim 1
Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 6
Theorem Illustration
Definition
Example MST
Safe Edges 1
Safe Edges 2
Safe Edges 3
⊲ Safe Edges 4
Kruskal 1
Kruskal 2
Prim 1
Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 7
Kruskal’s Algorithm
Definition
Example MST
Safe Edges 1
Safe Edges 2
Safe Edges 3
Safe Edges 4
⊲ Kruskal 1
Kruskal 2
Prim 1
Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 8
Kruskal Illustration
Definition
Example MST
Safe Edges 1
Safe Edges 2
Safe Edges 3
Safe Edges 4
Kruskal 1
⊲ Kruskal 2
Prim 1
Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 9
Prim’s Algorithm
Definition
Example MST
Safe Edges 1
Safe Edges 2
Safe Edges 3
Safe Edges 4
Kruskal 1
Kruskal 2
⊲ Prim 1
Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 10
Prim Illustration
Definition
Example MST
Safe Edges 1
Safe Edges 2
Safe Edges 3
Safe Edges 4
Kruskal 1
Kruskal 2
Prim 1
⊲ Prim 2
CS 3343 Analysis of Algorithms Minimum Spanning Trees – 11
