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Topic 12

Topic 12. Graphs 1. Graphs. Definition: Two types:. Undirected. Directed. Examples/Applications. Transportation Networks. Shortest path?. Source: pages.cs.wisc.edu. Vacuum World (from AI). What belief states could we be in if we do a certain sequence of actions?.

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Topic 12

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  1. Topic 12 Graphs 1

  2. Graphs • Definition: • Two types:

  3. Undirected

  4. Directed

  5. Examples/Applications

  6. Transportation Networks Shortest path? Source: pages.cs.wisc.edu

  7. Vacuum World (from AI) What belief states could we be in if we do a certain sequence of actions? Source: centurion2.com

  8. Social Network Are you an introvert? Who are you most friendly with? Source: infosthetics.com

  9. Graphical Models (from machine learning) What was the most likely sequence of weather given the actions (walking, shopping, cleaning) on those days? Source: wikipedia.org

  10. Graphical Models What is the most probable configuration that created this image? Source: PRML by Christopher Bishop

  11. More Definitions • Path: • Length:

  12. Cycle: • Self-loop:

  13. Incident edges

  14. Simple graph: • Acyclic graph:

  15. Subgraph: • Forest: • Tree

  16. Connected: • Complete graph:

  17. Weighted graph:

  18. Announcements • Homework 6 due • Test on Thursday (material up to Tuesday) • Reminder: survey • Review on Wednesday

  19. Announcements • Survey • Quizzes/Graph sample problems online • Participation

  20. Graph Representations

  21. Adjacency Matrix (undirected)

  22. Storing for Undirected

  23. Adjacency Matrix (directed) Pros: Cons:

  24. Adjacency Matrix Costs • Space: • Adjacency check: • Listing edges of node:

  25. Adjacency list (undirected)

  26. Adjacency list (directed)

  27. Adjacency List Costs • Space: • Adjacency check: • Listing edges of node:

  28. Graph Search/Traversals • How do get from one node to another? • Why?

  29. Idea • Layers:

  30. Breadth First Search: Algorithm

  31. Example

  32. BFS Tree

  33. Depth-First Search • Applications: • Running time:

  34. Recursive Algorithm

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