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Alyce Brady CS 510: Computer Algorithms

Breadth-First Graph Traversal Algorithm. Alyce Brady CS 510: Computer Algorithms. Search: Look for a given node stop when node found, even if not all nodes were visited Traversal: Always visit all nodes. Search vs Traversal. Similar to Breadth-first Traversal of a Binary Tree

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Alyce Brady CS 510: Computer Algorithms

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  1. Breadth-First Graph Traversal Algorithm Alyce Brady CS 510: Computer Algorithms

  2. Search: Look for a given node stop when node found, even if not all nodes were visited Traversal: Always visit all nodes Search vs Traversal

  3. Similar to Breadth-first Traversal of a Binary Tree Choose a starting vertex Search all adjacent vertices Return to each adjacent vertex in turn and visit all of its adjacent vertices Breadth-first Search

  4. breadth-first-search mark starting vertex as visited; put on queue while the queue is not empty dequeue the next node for all unvisited vertices adjacent to this one mark vertex as visited add vertex to queue Pseudo-Code forBreadth-First Search

  5. Breadth-First Search Queue: A B C Current: D E F G

  6. Breadth-First Search Queue: v A A B C Current: D E F G

  7. Breadth-First Search Queue: v A A B C Current: D E F G A

  8. Breadth-First Search Queue: v A B C Current: D E F G A A

  9. Breadth-First Search Queue: v B A v B C Current: D E F G A A

  10. Breadth-First Search Queue: v C B A v v B C Current: D E F G A A

  11. Breadth-First Search Queue: v C B A v v B C Current: D E F G B A

  12. Breadth-First Search Queue: v C A v v B C Current: D E F G B A B

  13. Breadth-First Search Queue: v C A v v B C Current: D E F G B A B

  14. Breadth-First Search Queue: v D C A v v B C v Current: D E F G B A B

  15. Breadth-First Search Queue: v E D C A v v B C v Current: D E F G B v A B

  16. Breadth-First Search Queue: v F E D C A v v B C v D E F G Current: v v B A B

  17. Breadth-First Search Queue: v F E D C A v v B C v D E F G Current: v v C A B

  18. Breadth-First Search Queue: v F E D A v v B C v D E F G Current: v v C A B C

  19. Breadth-First Search Queue: v F E D A v v B C v D E F G Current: v v C A B C

  20. Breadth-First Search Queue: v F E D A v v B C v D E F G Current: v v C A B C

  21. Breadth-First Search Queue: v G F E D A v v B C v v D E F G Current: v v C A B C

  22. Breadth-First Search Queue: v G F E D A v v B C v v D E F G Current: v v D A B C

  23. Breadth-First Search Queue: v G F E A v v B C v v D E F G Current: v v D A B C D

  24. Breadth-First Search Queue: v G F E A v v B C v v D E F G Current: v v D A B C D

  25. Breadth-First Search Queue: v G F E A v v B C v v D E F G Current: v v D A B C D

  26. Breadth-First Search Queue: v G F E A v v B C v v D E F G Current: v v E A B C D

  27. Breadth-First Search Queue: v G F A v v B C v v D E F G Current: v v E A B C D E

  28. Breadth-First Search Queue: v G F A v v B C v v D E F G Current: v v E A B C D E

  29. Breadth-First Search Queue: v G F A v v B C v v D E F G Current: v v E A B C D E

  30. Breadth-First Search Queue: v G F A v v B C v v D E F G Current: v v F A B C D E

  31. Breadth-First Search Queue: v G A v v B C v v D E F G Current: v v F A B C D E F

  32. Breadth-First Search Queue: v G A v v B C v v D E F G Current: v v F A B C D E F

  33. Breadth-First Search Queue: v G A v v B C v v D E F G Current: v v F A B C D E F

  34. Breadth-First Search Queue: v G A v v B C v v D E F G Current: v v G A B C D E F

  35. Breadth-First Search Queue: v A v v B C v v D E F G Current: v v G A B C D E F G

  36. Breadth-First Search Queue: v A v v B C v v D E F G Current: v v G A B C D E F G

  37. Breadth-First Search A B C D E F G A B C D E F G

  38. Was this a true search? How would we make it a true search? Was this a true traversal? How would we make it a true traversal?

  39. Time Complexity Adjacency Lists Each node is added to queue once Each node is checked for each incoming edge O (v + e) Adjacency Matrix Have to check all entries in matrix: O(n2) Time and Space Complexityfor Breadth-First Search

  40. Space Complexity Queue to handle unexplored nodes Worst case: all nodes put on queue (if all are adjacent to first node) O(n) Time and Space Complexityfor Breadth-First Search

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