1 / 25

Fully PTAS Knapsack Decision Version Proof Theorem Algorithm

Learn about the proof and theorem of the Fully PTAS for the Knapsack Decision Version algorithm, its complexity, and the classification and implementation details.

williamsjames
Download Presentation

Fully PTAS Knapsack Decision Version Proof Theorem Algorithm

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 25 Partition

  2. Partition

  3. Subsum

  4. S=33333333333333333333 1111111111111111111111 1 1

  5. Puzzle Answer

  6. Knapsack

  7. Decision Version

  8. Theorem Proof.

  9. Theorem

  10. Algorithm • Classify: for i < m, ci< a= cG, for i > m+1, ci > a. • Sort • For

  11. Proof.

  12. Time

  13. Fully PTAS • A problem has a fully PTAS if for any ε>0, it has (1+ε)-approximation running in time poly(n,1/ε).

  14. Fully FTAS for Knapsack

  15. 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

More Related