1. Lecture 13 CSE 331 Oct 2, 2009

2. Announcements Mid term in < 2 weeks Graded HW2 at the END of the class

3. Breadth First Search (BFS) Is s connected to t? Build layers of vertices connected to s L 0 = {s} Assume L 0,..,L j have been constructed L j+1 set of vertices not chosen yet but are connected to L j Stop when new layer is empty L j : all nodes at distance j from s

4. BFS Tree BFS naturally defines a tree rooted at s L j forms the jth “level” in the tree u in L j+1 is child of v in L j from which it was “discovered” 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 1 1 2 2 3 3 L0L0 L1L1 4 4 5 5 7 7 8 8 L2L2 6 6 L3L3

5. Questions?

6. A theory workshop this weekend http://www.cse.buffalo.edu/events/theory-III/

7. Proofs in the lectures Mostly proof ideas from now on Read the book for the formal proofs Homeworks will still require formal proofs

8. Connected Component Connected component (of s) is the set of all nodes connected to s

9. Computing Connected Component Start with R = {s} While exists (u,v) edge v not in R and u in R Add v to R Output R

10. Today’s agenda If w is in R iff w is connected to s Depth First Search Computing all connected components

11. How is BFS related to this algo?

12. A DFS run 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 1 1 2 2 4 4 5 5 6 6 3 3 8 8 7 7 Every non- tree edge is between a node and its ancestor DFS tree

13. Questions?

14. Connected components are disjoint Either Connected components of s and t are the same or are disjoint Algorithm to compute ALL the connected components? Run BFS on some node s. Then run BFS on t that is not connected to s