1. Lecture 15
CSE 331
Oct 3, 2011

2. Mid term Next Monday in class Unfortunately I won’t be there
Jiun-Jie with my PhD students Steve & Swapnoneel will proctor the exam

3. Feedback Response-I I’ll use the microphone today
Let me know via poll on the blog if it worked better

4. Graphs will help us here
Feedback Response-II
Problem Statement
Real world problem
Graphs will help us here
Problem Definition
Precise mathematical def
Algorithm
“Implementation”
Data Structures
Analysis
Correctness/Run time

5. Feedback Response-III
The workload is “insane” and I might be unaware of it
Syllabus states that you’re supposed to spend at least 8-12 hours
outside of the lectures
If you’re spending much more time than above, please come and talk
to me
I’m aware that ideal situations do not always exists
More chances for you to “make-up” in the course

6. Mid term entry Has been posted on the blog
Don’t read too much into the content
of the sample mid-term

7. On Friday, Oct 7 hours-a-thon Atri: 2:00-3:00 (Bell 123)
Jiun-Jie: 4:00-5:00 (Commons 9)
Jesse: 5:00-6:00 (Bell 224)

8. Empty Slots Coming up…

9. Graph representations1
Better for sparse graphs and traversals
Adjacency matrix
Adjacency List
(u,v) in E?
O(1)
O(n) [ O(nv) ]
All neighbors of u?
O(n)
O(nu)
O(n2)
Space?
O(m+n)

10. 2 # edges = sum of # neighbors
2m = Σ u in V nu
Rest of the graph
Give 2 pennies to each edge
Total # of pennies = 2m
nv=3 u
nu=4 v
Each edges gives one penny to its end points
# of pennies u receives = nu

11. Questions?

12. Today’s agenda
Run-time analysis of BFS

13. Breadth First Search (BFS)
Build layers of vertices connected to s
L0 = {s}
Assume L0,..,Lj have been constructed
Lj+1 set of vertices not chosen yet but are connected to Lj
Use CC[v] array
Stop when new layer is empty
Use linked lists

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

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

16. A DFS run using an explicit stack7 8 1 7 7 6 3 2 3 5 8 4 4 5 5 3 6 2 3 1

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

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

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

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

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