Graph Traversal for Pathfinding:
Greedy Algorithms & Trolley Problems
Start
Section I
Topic: Greedy Algorithm
What's the heck is that.
Greedy Algorithms ...
A simple, inuative algorithm to optimize selection. The Greedy Algorithm begins from the first vertex and chooses the path with the next largest vertex or edge. The final result often isnt the largest beacuse it cannot see the whole graph
Greedy Path: 7-12-6 Optimal Path: 3-99 Greedy sum: 30 Optimal Sum: 102
Section II
Dijkstra's Algorithm
What the heck is that?
Dijkstra's Algorithms ...
A simple, inuative algorithm to optimize selection. Creates a tree of shortest paths from the starting vertex, the source, to all other points in the graph.
Path from a-b: 1-3-6-5 Sum of optimal path: 20
Section III
Trolley Time!
Greedy Algorithm
Edge 1
Edge 2
Choice 1
Which next vertex do you choose?
Edge 1
Edge 2
Choice 2
Which next vertex do you choose?
Edge 1
Edge 2
Choice 2
Which next vertex do you choose?
Edge 1
Edge 2
Choice 4
Which next vertex do you choose?
Edge 1
Edge 2
Choice 5
Which next vertex do you choose?
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Uber & Navigational Mapping
Practical Applications
Estimate arrival times (ETA) by representing road networks as graphs with nodes at intersections and weights representing travel time or distance, using A*.
A* uses hueristic search techinque unlike Dijkstra's.
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Transcript
Graph Traversal for Pathfinding:
Greedy Algorithms & Trolley Problems
Start
Section I
Topic: Greedy Algorithm
What's the heck is that.
Greedy Algorithms ...
A simple, inuative algorithm to optimize selection. The Greedy Algorithm begins from the first vertex and chooses the path with the next largest vertex or edge. The final result often isnt the largest beacuse it cannot see the whole graph
Greedy Path: 7-12-6 Optimal Path: 3-99 Greedy sum: 30 Optimal Sum: 102
Section II
Dijkstra's Algorithm
What the heck is that?
Dijkstra's Algorithms ...
A simple, inuative algorithm to optimize selection. Creates a tree of shortest paths from the starting vertex, the source, to all other points in the graph.
Path from a-b: 1-3-6-5 Sum of optimal path: 20
Section III
Trolley Time!
Greedy Algorithm
Edge 1
Edge 2
Choice 1
Which next vertex do you choose?
Edge 1
Edge 2
Choice 2
Which next vertex do you choose?
Edge 1
Edge 2
Choice 2
Which next vertex do you choose?
Edge 1
Edge 2
Choice 4
Which next vertex do you choose?
Edge 1
Edge 2
Choice 5
Which next vertex do you choose?
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Vertex 1
Vertex 2
Vertex 3
Vertex 4
Vertex 5
Your Winnings!
Uber & Navigational Mapping
Practical Applications
Estimate arrival times (ETA) by representing road networks as graphs with nodes at intersections and weights representing travel time or distance, using A*.
A* uses hueristic search techinque unlike Dijkstra's.
Got an idea?
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