1. Lecture 39
CSE 331
Dec 5, 2011

2. Review Sessions etc. Atri: (at least ½ of) class Friday
Jiun-Jie: Extra office hour Friday
Jesse: Review Session on Mon, Dec 12 (pick time slot on blog)
All grades have been uploaded to UBLearns
Temp grades hopefully by end of this week

3. All you ever wanted to know about the final exam…

4. Need volunteers for today

5. Longest path problem
Given G, does there exist a simple path of length n-1 ?

6. Longest vs Shortest Paths

7. Two sides of the “same” coin
Shortest Path problem
Can be solved by a polynomial time algorithm
Is there a longest (simple) path of length n-1?
Given a path can verify in polynomial time if the answer is yes

8. Poly time algo for longest path?

9. Alternate NP definition: Guess witness and verify!
P vs NP question
P: problems that can be solved by poly time algorithms
Is P=NP?
NP: problems that have polynomial time verifiable witness to optimal solution
Alternate NP definition: Guess witness and verify!

10. Pretty much all known proof techniques provably will not work
Proving P ≠ NP
Pick any one problem in NP and show it cannot be solved in poly time
Pretty much all known proof techniques provably will not work

11. Proving P = NP Will make cryptography collapse
Compute the encryption key!
Prove that all problems in NP can be solved by polynomial time algorithms NP
Solving any ONE problem in here in poly time will prove P=NP!
NP-complete problems

12. If you are curious for more
CSE431: Algorithms
CSE 396: Theory of Computation

13. Nice survey on P vs. NP

14. Today’s agenda
Overview of how things work in the P vs NP world