1. Lecture 23
CSE 331
Oct 28, 2009

2. Feedback forms Please pick one up
You will have last 5 minutes in the class to fill it in

3. Warning More work for YOU I am running behind on my topics schedule
I wanted to show some of the cooler stuff
Will not always do COMPLETE proofs
More work for YOU

4. Last lecture
Convert optimal schedule O to Ô such that Ô has no inversions
(a) Exists an inversion (i,j) such that i is scheduled right before j (di > dj)
Repeat O(n2) times
(a.5) Swap i and j to get O’
Exercise: Prove by induction.
No consecutive inversion 
No inversions
(b) O’ has one less inversion than O
(c) Max lateness(O’) ≤ Max lateness(O)

6. Max lateness(O’) ≤ Max lateness(O)
di > dj
Same lateness
Same lateness O i j t1 t3 O’ j i t2
Lateness of j in O’ ≤ Lateness of j in O
Lateness of i in O’ ≤ Lateness of j in O
Lateness of i in O’ =
t3 - di
< t3 - dj
= Lateness of j in O

7. Rest of today
Shortest Path Problem

8. Reading Assignment
Sec 2.5of [KT]