1. Lecture 19
CSE 331
Oct 14, 2011

2. Announcements
Graded HW 4 next Th onwards
HW 5 has been posted

3. Mid Term stuff Graded mid term at the end of the lecture
Mid term post up on the blog
Read it before asking for regrade requests
A temp grade assigned by next week
I’ll ask some of you to meet me in person

4. Sign up for scribe/blog post

5. Interval Scheduling Problem
Input: n intervals [s(i), f(i)) for 1≤ i ≤ n
Output: A schedule S of the n intervals
No two intervals in S conflict
|S| is maximized

6. Analyzing the algorithm
R: set of requests
A* has no conflicts
Set A to be the empty set
While R is not empty
Choose i in R with the earliest finish time
A* is an optimal solution
Add i to A
Remove all requests that conflict with i from R
Return A* = A

7. Greedy “stays ahead”
Greedy
OPT

8. What can you say about f(i1) and f(j1)?
Greedy “stays ahead”
A* = i1,…,ik
O = j1,…,jm
k = m
What do we need to prove?
What can you say about f(i1) and f(j1)?

9. A formal claim For every r ≤ k, f(ir) ≤ f(jr) A* = i1,…,ik O = j1,…,jm
The greedy algorithm outputs an optimal A
Proof by contradiction: A is not optimal
A* = i1,…,ik
O = j1,…,jm
m > k
After ik, R was non-empty! ik
No conflict! jk
jk+1

10. Today’s agenda Analyze run-time of the greedy algorithm
Prove the claim
Analyze run-time of the greedy algorithm

11. The mid-term mixup
Proctors allowed early arrivals to read the exam questions
Unfair to students who did not come early
Proposal: I’ll add 5 points at the end of the semester if it bumps up a letter grade
(but not from A- to A)
me if you have comments

12. The mid-term story Average: 50.2 Median: 51
Remember, mid term score gets dropped if you better on the final
Time pressure issues

13. Greedy can always pick jr
Proof of claim
For every r ≤ k, f(ir) ≤ f(jr)
Why is r=1 OK?
By induction on r
Assume true up to r-1
Greedy can always pick jr ?
ir-1 ir
jr-1 jr