1 / 53
Télécharger la présentation

Exploring Graphs: Definitions, Types, and Applications

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related