1. Lecture 36
CSE 331
Nov 30, 2016

2. Quiz 2 on Monday

3. Official Feedback forms

4. We need volunteers!

5. Scheduling to min idle cycles
n jobs, ith job takes wi cycles
You have W cycles on the cloud
What is the maximum number of jobs you can schedule?

6. When to use Dynamic Programming
O(nW) runtime
There are polynomially many sub-problems
OPT(j,W’) 0 ≤ j ≤ n, 0 ≤ W’ ≤ W
Richard Bellman
Optimal solution can be computed from solutions to sub-problems
OPT(j, W’) = …
There is an ordering among sub-problem that allows for iterative solution
OPT (j,W’) only depends on OPT(j-1, 0), …, OPT(j-1,W)

7. Is O(nW) polynomial time?
Pseudo-polynomial
n jobs, ith job takes wi cycles
You have W cycles on the cloud
log W bits needed
What is the maximum number of jobs you can schedule?

8. Shortest Path Problem
Input: (Directed) Graph G=(V,E) and for every edge e has a cost ce (can be <0)
t in V
Output: Shortest path from every s to t
Assume that G has no negative cycle 1
100
-1000
899 s t
Shortest path has cost negative infinity

9. Today’s agenda
Dynamic Program for shortest path

10. May the Bellman force be with you