1. ENGM 631 Minimum Spanning Tree

2. Prototype Example Seervada Park Trams route smallest total distance Phone lines minimum spanning tree Tram limitations for environmental concerns limitations on each road Maximum Flow problem O is origin, T is endpoint

3. Prototype Example

4. Other Shortest-Path Uses Minimize Total distance Minimize Total cost of travel Minimize Total time of travel Used in directed networks To every node methods exist To and from every node exist, too

5. Minimum Spanning Tree

6. 9.4 Minimum Spanning Tree

7. Applications 1.Telecommunications networks (fiber- optic, computer, telephone, cable TV) 2.Lightly used transportation networks 3.High voltage power transmission lines 4.Wiring on electrical equipment 5.Design of pipelines to connect locations

8. Algorithm Min Span Tree It’s a simple greedy algorithm Just pick the smallest link and attach to the tree

9. Algorithm Min Span Tree

10. Span Tree for Park Ex.