1. Lecture 13
CSE 331
Oct 1, 2012

2. Reminders
HW 2 ready for pickup
MID TERM IN 2.5 WEEKS (in class)

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

4. 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

5. Algorithm motivation
all

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

7. Questions?

8. Breadth First Search (BFS)
Which vertices is s connected to?
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

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

10. 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

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

12. Algo to compute the connected component of s?

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