topic 12 graphs 1. graphs definition: two types:
TRANSCRIPT
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Topic 12
Graphs 1
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Graphs
• Definition:
• Two types:
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Undirected
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Directed
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Examples/Applications
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Transportation Networks
Source: pages.cs.wisc.edu
Shortest path?
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Vacuum World (from AI)
Source: centurion2.comWhat belief states could we be in if we do a certain sequence of actions?
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Social Network
Source: infosthetics.comAre you an introvert? Who are you most friendly with?
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Graphical Models (from machine learning)
Source: wikipedia.org
What was the most likely sequence of weather given the actions (walking, shopping, cleaning) on those days?
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Graphical Models
Source: PRML by Christopher BishopWhat is the most probable configuration that created this image?
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More Definitions• Path:
• Length:
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• Cycle:
• Self-loop:
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• Incident edges
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• Simple graph:
• Acyclic graph:
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• Subgraph:
• Forest:
• Tree
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• Connected:
• Complete graph:
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• Weighted graph:
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Graph Representations
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Adjacency Matrix (undirected)
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Adjacency Matrix (directed)
Pros: Cons:
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Adjaceny list (undirected)
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Adjaceny list (directed)
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Adjacency List Costs
• Space:
• Searching for edge between nodes:
• Adjacency check:
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Graph Search/Traversals
• How do get from one node to another?
• Why?
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Breadth First Search
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Implementing BFS
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Depth-First Search
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Recursive Algorithm
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Iterative Algorithm