1. Lecture 19
CSE 331
Oct 13, 2010

2. Online Office hours
Tonight 9:30-10:30pm

3. On Friday, Oct 15 hours-a-thon Atri: 2:00-3:30 (Bell 123)
Jeff: 3:30-5:00 (Commons 9)
Alex: 5:00-6:30 (Bell 224)

4. Polls on the blog
In my blog post for Lect 18

5. O(m+n) BFS Implementation
Input graph as Adjacency list
BFS(s)
Array
CC[s] = T and CC[v] = F for every v≠ u
Set i = 0
Set L0= {s}
While Li is not empty
Linked List
Li+1 = Ø
For every u in Li
Consider every edge (u,v)
If CC[v] = F then
CC[v] = T
Add v to Li+1
i++

6. All layers are considered in first-in-first-out order
All the layers as one
BFS(s)
All layers are considered in first-in-first-out order
CC[s] = T and CC[v] = F for every v≠ u
Set i = 0
Set L0= {s}
While Li is not empty
Li+1 = Ø
For every u in Li
Can combine all layers into one queue: all the children of a node are added to the end of the queue
For every edge (u,v)
If CC[v] = F then
CC[v] = T
Add v to Li+1
i++

7. An illustration 1 2 3 4 5 7 8 6 1 7 2 3 8 4 5 6

8. Implementing DFS in O(m+n) time
Same as BFS except stack instead of a queue

9. Reading Assignment
Sec 3.3, 3.4 and 3.5 of [KT]

10. Directed graphs Model asymmetric relationships
Precedence relationships
u needs to be done before v means (u,v) edge

11. Directed graphs Adjacency matrix is not symmetric
Each vertex has two lists in Adj. list rep.

12. Directed Acyclic Graph (DAG)
No directed cycles
Precedence relationships are consistent

13. Topological Sorting of a DAG
Order the vertices so that all edges go “forward”