1. Revisit Dynamic Programming

3. Technique 1
Find a related optimization problem with self-reducibility.
Solve the related problem by dynamic programming.
Solve original problem.

4. A problem on strip: outside weighted disks cover
Inside points with minimum total weight. L p2 p1 pi
Ti(D,D’) : minimum weight set
with D, D’, dominating p1, …, pi such that
(1) D (lowest intersection point on L)
among disks above the strip
(2) D’(highest intersection point on L)
among disks below the strip

5. D1 (lowest intersection point on L)
among disks above the strip, in Ti(D,D’) L p2 p1
pi-1
D2 (highest intersection point on L)
among disks below the strip, in Ti(D,D’)

6. Dynamic Programming

7. Dynamic Programming

8. D1
pi-1 pi pj D

9. Pseudo Polynomial-time Algorithm for Knapsack

10. DP-type Algorithm

11. Initially,

14. Time outside loop: O(n) Inside loop: O(nM) where M=max ci
Core: O(n log (MS))
Total O(n M log (MS))
Since input size is O(n log (MS)), this is a pseudo-polynomial-time due to M=2 3
log M

15. Running time
(1) Time for computing one element with recursive formula.
(2) Size of the table.
Running time = (1) x (2)

16. Technique 2 Speed Up