Loading in 5 sec....

PTAS(Polynomial Time Approximation Scheme) cont.PowerPoint Presentation

PTAS(Polynomial Time Approximation Scheme) cont.

- By
**meena** - Follow User

- 136 Views
- Uploaded on

Download Presentation
## PowerPoint Slideshow about ' PTAS(Polynomial Time Approximation Scheme) cont.' - meena

**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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

PTAS vs FPTAS

- PTAS requires the complexity of an algorithm to be polynomial in terms of input size n for a fixed approximation factor є
- FPTAS requires the complexity of an algorithm to be polynomial, both in terms of n as well as 1/є

Designing Polynomial Time Approximation Scheme for Sub-set Sum Problem

- Input
- Output

Designing Polynomial Time Approximation Scheme for Sub-set Sum Problem

- In case of approximation, we are interested in a S’ such that
- We define, Libe the set of numbers that are sum of all elements in each possible subsets of set Si where, Si is a set of first ith elements in set S. Then,

Designing Polynomial Time Approximation Scheme for Sub-set Sum Problem

- Pseudo-code for finding the closest sub-sum can be
- While i<n
- Remove where, lj is any element in set Li
- end while

- Solution: last element of Ln
- Complexity: O(nW)

Designing Polynomial Time Approximation Scheme for Sub-set Sum Problem

- Complexity is O(nW), W can be exponential in the worst-case!
- Consider small intervals instead of exact values in Li?
- Equally spaced vs expanding intervals?
- Possible to maintain an approximation factor?

To be cont. in next lecture…

Download Presentation

Connecting to Server..