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lec0504-GraphAlgorithms

# lec0504-GraphAlgorithms - Announcements MP7 due 5/4 11:59p...

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Announcements: MP7 due 5/4, 11:59p. Final exam: 5/11, 7-10p, rooms on web. Review sessions: 5/4, 7-10p, 1404 Siebel 5/8, 3-5p, 1404 Siebel Today: Graphs – Minimum Spanning Trees Single Source Shortest Path

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How do we get from here to there? Need: 1. Common Vocabulary 2. Graph implementation 3. Traversal-DFS, BFS 4. Algorithms. a) MST b) Shortest Path
Minimum Spanning Tree Algorithms: •Input: connected, undirected graph G with unconstrained edge weights •Output: a graph G’ with the following characteristics - •G’ is a spanning subgraph of G •G’ is connected and acyclic (a tree) •G’ has minimal total weight among all such spanning trees C B A E D F 4 8 7 1 2 5 2 3 9

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Example of Prim’s algorithm - B D C A F E 7 4 2 8 5 7 3 9 8 Initialize structure: 1. For all v, d[v] = “infinity”, p[v] = null 2. Initialize source: d[s] = 0 3. Initialize priority (min) queue 4. Initialize set of labeled vertices to . Repeat these steps n times:
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lec0504-GraphAlgorithms - Announcements MP7 due 5/4 11:59p...

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