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## The Minimum Cost Spanning Tree Problem

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### The relationship between shortest path and matrix multiplication. Faster-All-Pairs-Shortest-Paths algorithm. Floyd-Warshall algorithm. Puzzle 1. Puzzle 2 ... – PowerPoint PPT presentation

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Title: The Minimum Cost Spanning Tree Problem

1
Lecture 11
• The Minimum Cost Spanning Tree Problem

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Correctness
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The Greedy Algorithm
• animation

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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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The Greedy Algorithm in Action
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Correctness
• The cut-optimality Condition

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Prims algorithm
• animation

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Prims Algorithm in Action
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The minimum cost arc from yellow nodes to green
nodes can be found by placing arc values in a
priority queue.
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Prims Algorithm in Action
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Prims Algorithm in Action
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Prims Algorithm in Action
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Prims Algorithm in Action
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Prims Algorithm in Action
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Prims Algorithm in Action
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Prims Algorithm in Action
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Prims Algorithm in Action
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Prims Algorithm in Action
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Correctness
• Cut-optimality Condition

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Sollins Algorithm
• animation

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Sollins Algorithm in Action
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Treat all nodes as singleton components, and then
select the min cost arc leaving the component.
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Sollins Algorithm in Action
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Find the min cost edge out of each component
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Appendix Priority Queue
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Priority Queue
• A priority queue is a data structure for
maintaining a set of elements, each with an
associated value, called a key.
• A min-priority queue supports the following
operations Insert(S,x), Minimum(S),
• Extract-Min(S), Increase-Key(S,x,k).
• Min-Heap can be used for implementing
• min-priority queue.

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