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PTAS(Polynomial Time Approximation Scheme) cont.

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PTAS(Polynomial Time Approximation Scheme) cont.

Prepared by, Umair S.

March 25th, 2009

- 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

- Input
- Output

- 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,

- 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)

- 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…