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

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Nov 25, 2022 147 likes •259 views

Minimum Spanning Trees Introduction Safe Edges Kruskals Algorithm Prims Algorithm CS 3343 Analysis of Algorithms Minimum Spanning Trees 1 Minimum Spanning Tree Definition Definition Example MST Safe Edges 1 Safe Edges 2 Safe

SLIDE 1

CS 3343 Analysis of Algorithms Minimum Spanning Trees – 1

Minimum Spanning Trees

Introduction Safe Edges Kruskal’s Algorithm Prim’s Algorithm

SLIDE 2

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

SLIDE 3

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

SLIDE 4

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

SLIDE 5

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

SLIDE 6

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

SLIDE 7

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

SLIDE 8

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

SLIDE 9

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

SLIDE 10

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

SLIDE 11

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