1. Prim’s Minimum Spanning Tree Algorithm Neil Tang 4/1/2008
CS223 Advanced Data Structures and Algorithms

2. CS223 Advanced Data Structures and Algorithms
Class Overview
The minimum spanning tree problem
An application
Prim’s algorithm
Implementation and time complexity
CS223 Advanced Data Structures and Algorithms

3. Minimum Spanning Tree Problem
The cost of a tree: The sum of the weights of all links on the tree.
The Minimum Spanning Tree (MST) problem: Given a weighted undirected graph G, find a minimum cost tree connecting all the vertices on the graph
CS223 Advanced Data Structures and Algorithms

4. Minimum Spanning Tree Problem
CS223 Advanced Data Structures and Algorithms

5. CS223 Advanced Data Structures and Algorithms
An Application
Broadcasting problem in Computer Networks: Find the minimum cost route to send a package from a source node to all the other nodes in the network.
CS223 Advanced Data Structures and Algorithms

6. CS223 Advanced Data Structures and Algorithms
Prim’s Algorithm
CS223 Advanced Data Structures and Algorithms

7. CS223 Advanced Data Structures and Algorithms
Prim’s Algorithm
CS223 Advanced Data Structures and Algorithms

8. CS223 Advanced Data Structures and Algorithms
Prim’s Algorithm
CS223 Advanced Data Structures and Algorithms

9. Implementation and Time Complexities
Difference between Prim and Dijkstra: 1) Arbitrarily pick a node to start with; 2) Relaxation dw=min(dw, cw,v)
Trivial: O(|V|2 + |E|) = O(|V|2)
Heap: deleteMin |V| times + decreaseKey |E| times
O(|V|log|V| + |E|log|V|) = O (|E|log|V|)
CS223 Advanced Data Structures and Algorithms