Minimum Spanning Trees Introduction Safe Edges Kruskals Algorithm - PowerPoint PPT Presentation

Minimum Spanning Trees Introduction Safe Edges Kruskal’s Algorithm Prim’s Algorithm CS 3343 Analysis of Algorithms Minimum Spanning Trees – 1

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