Connected Components Minimum Spanning Tree

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Presentation transcript:

Connected Components Minimum Spanning Tree Graph Algorithms 1 Connected Components Minimum Spanning Tree

Problem: Connected Components Instance: Given an undirected graph G=(V,E) Question: Print out the sets of vertices that are connected to each other. Note: A vertex u is connected to a vertex v iff there is a path connecting the vertices.

Connected Components Algorithm

Problem: Strongly Connected Components Instance: Given an directed graph G=(V,E) Question: Print out the sets of vertices that are connected to each other. Note: A vertex u is connected to a vertex v iff there is a path connecting the u to v and a path from v to u.

Strongly Connected - Algorithm

Problem: Minimum Spanning Tree Instance: Given a graph G=(V,E) Question: What is the minimum edge weight subgraph G’=(V,E’) that can be constructed from G such that the graph G’ is connected?

Kruskel’s Algorithm for MST

Kruskel’s Algorithm Code

Prim’s Algorithm for MST

Prim’s Algorithm - Code

Prim’s Algorithm - Analysis