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Section 9

Section 9. Graph search algorithms. Breadth-first search. Idea: Let |n| denote a distance of node n from the initial node. We visit nodes in order: All nodes n such that |n| = 1 All nodes n such that |n| = 2 All nodes n such that |n| = 3 All nodes n such that |n| = 4

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Section 9

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  1. Section 9 • Graph search algorithms

  2. Breadth-first search • Idea: Let |n| denote a distance of node n from the initial node. We visit nodes in order: • All nodes n such that |n| = 1 • All nodes n such that |n| = 2 • All nodes n such that |n| = 3 • All nodes n such that |n| = 4 • All nodes n such that |n| = 5 ....

  3. BFS: Water analogy • BFS is similar to pouring water! • We pour the water on the first node. When there is too much water in it, the nodes adjacent to it start to fill. And so on...

  4. BFS

  5. Depth-first search • Idea: We go as deep as possible. • Visit recursively all the adjacent nodes of the source node.

  6. DFS: Labyrinth analogy • DFS is similar to going through labyrinth. • We walk leaving a thread behind us. Whenever we have the choice of path, we choose the leftmost one. If we reach a dead-end or the place already marked, we go back to the first unvisited place.

  7. DFS

  8. BFS + DFS • Stunning fact - we can implement both of them using the same code, changing only the underlying SequenceStructure.

  9. BFS + DFS • initialize toDo with the node we are starting from while (!empty(toDo)) { remove a node n from toDo visit(n) put all unvisited neighbours of n on toDo }

  10. BFS + DFS

  11. Best-first search • In situation when we have a weight function f on nodes, which tells us which node to visit first. • BFS, but visiting neighbours according to the fumction f. • Just use priority queue!

  12. WWW as a graph • Nodes - • Edges -

  13. WWW as a graph • Nodes - webpages • Edges - links

  14. WWW as a graph • How to write a program downloading a whole web page?

  15. WWW as a graph • How to write a program downloading a whole web page? • Use graph search! • Which one?

  16. WWW as a graph • How to write a program downloading a whole web page? • Use graph search! • Which one? • BFS!

  17. WWW as a graph • Interesting questions: • What is the diameter of the graph? (probably about 20) • What is its structure? • What are the efficient search algorithms? - Google, Altavista • What is a „typical” node? • Many more...

  18. Bus/train map as a graph • Nodes - • Edges -

  19. Bus map as a graph • Nodes - bus/train stops/stations • Edges - there’s an edge from one node to the other if there is a bus/train, which takes you from one stop to the other. • www.bahn.de • How to find how to reach a bus stop/city?

  20. Survival skills • How to find a way out in the labyrinth? • Optimistic version: With a thread of string. • Pessimistic version: Without a thread.

  21. With a thread • Use DFS - using a thread to go back to the yet unvisited paths.

  22. Without a thread • A heuristics which often works - always turn left.

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