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Graphs – Searching for Relationships COMP 200 & COMP 130 John Greiner & Stephen Wong

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Graphs – A Reminder Vertices/nodes + edges connecting vertices 1 3 2 5 4 Directed 1 3 2 5 4 Undirected

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Social graph How are you connected to someone else? Math co-authors, centered on Paul Erdös.

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Can Introducing Hepocyte Growth Factor Lead to Apoptosis?

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How are Two Species Related?

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Discovering Your Own Relations 7

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How to Solve a Maze? 8

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Solving a Maze: Right-Hand Rule 9 Good when you don’t know the maze layout.

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How to Get to Work? 10

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How to Route Email?

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Focus on Three Algorithms Depth-first Search Breadth-first Search Dijkstra’s Shortest Path 12 First, just quick introductions to each.

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Depth- vs. Breadth-First Search 13 17 2 3 8 9 5 4 6 12c 2b 2a 3c 4b 3b 3a 4a DFSBFS

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Dijkstra’s Shortest Path 14 4 5 3 2 7 1 8 2 3 4 0

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Dijkstra’s Shortest Path 15 4 5 3 2 7 1 8 2 3 4 0 7? 3? 4?

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Dijkstra’s Shortest Path 16 4 5 3 2 7 1 8 2 3 4 0 7? 3 4?

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Dijkstra’s Shortest Path 17 4 5 3 2 7 1 8 2 3 4 0 5? 3 4? 8?

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Dijkstra’s Shortest Path 18 4 5 3 2 7 1 8 2 3 4 0 5? 3 4 8?

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Dijkstra’s Shortest Path 19 4 5 3 2 7 1 8 2 3 4 0 5? 3 4 8? 6? 12?

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Dijkstra’s Shortest Path 20 4 5 3 2 7 1 8 2 3 4 0 5 3 4 8? 6? 12?

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Dijkstra’s Shortest Path 21 4 5 3 2 7 1 8 2 3 4 0 5 3 4 8? 6 12?

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Dijkstra’s Shortest Path 22 4 5 3 2 7 1 8 2 3 4 0 5 3 4 8 6 12?

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Dijkstra’s Shortest Path 23 4 5 3 2 7 1 8 2 3 4 0 5 3 4 8 6 9?

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Dijkstra’s Shortest Path 24 4 5 3 2 7 1 8 2 3 4 0 5 3 4 8 6 9

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Dijkstra’s Shortest Path 25 4 5 3 2 7 1 8 2 3 4 0 5 3 4 8 6 913? 12?

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Dijkstra’s Shortest Path 26 4 5 3 2 7 1 8 2 3 4 0 5 3 4 8 6 913? 12

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Dijkstra’s Shortest Path 27 4 5 3 2 7 1 8 2 3 4 0 5 3 4 8 6 913 12

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