1. Lecture 15
CSE 331
Oct 4, 2010

2. Announcements Final exam: Dec 14, 3:30pm-6:30pm, Knox 104
Mid term: Oct 18, in class
Graded HW 2 on Wed: sorry!

3. not student post category

4. Determining connectivity in graphs s t
Are s and t connected?

5. Brute-force algorithm
List all possible distinct vertex sequences between s and t
n! such sequences
Check if any is a path between s and t

6. Algorithm motivation
all

7. Distance between u and v
Length of the shortest length path between u and v
Distance between RM and BO? 1

8. Questions?

9. Breadth First Search (BFS)
Is s connected to t?
Build layers of vertices connected to s
Lj : all nodes at distance j from s
L0 = {s}
Assume L0,..,Lj have been constructed
Lj+1 set of vertices not chosen yet but are connected to Lj
Stop when new layer is empty

10. Exercise for you
Prove that Lj has all nodes at distance j from s

11. Given BFS, how to decide if s is connected to t?

12. BFS Tree BFS naturally defines a tree rooted at s Add non-tree edges
Lj forms the jth “level” in the tree
u in Lj+1 is child of v in Lj from which it was “discovered” 1 7 1 L0 2 3 L1 2 3 8 4 5 4 5 7 8 L2 6 6 L3

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

14. Algo to compute the connected component of s?

15. Today’s agenda Every edge in is between consecutive layers
Computing Connected component