CS223-0401-Prim

# CS223-0401-Prim - Broadcasting problem in Computer Networks...

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

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CS223 Advanced Data Structures and Algorithms 2 Class Overview 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 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

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CS223 Advanced Data Structures and Algorithms 4 Minimum Spanning Tree Problem Minimum Spanning Tree Problem
CS223 Advanced Data Structures and Algorithms 5 An Application An Application

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Unformatted text preview: 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 Prim’s Algorithm Prim’s Algorithm CS223 Advanced Data Structures and Algorithms 7 Prim’s Algorithm Prim’s Algorithm CS223 Advanced Data Structures and Algorithms 8 Prim’s Algorithm Prim’s Algorithm CS223 Advanced Data Structures and Algorithms 9 Implementation and Time Complexities Implementation and Time Complexities Difference between Prim and Dijkstra: 1) Arbitrarily pick a node to start with; 2) Relaxation d w =min(d w , c w,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|)...
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CS223-0401-Prim - Broadcasting problem in Computer Networks...

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