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PTAS(Polynomial Time Approximation Scheme) cont. Prepared by, Umair S. March 25 th , 2009. 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

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ptas polynomial time approximation scheme cont

PTAS(Polynomial Time Approximation Scheme) cont.

Prepared by, Umair S.

March 25th, 2009

ptas vs fptas
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 problem1
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 problem2
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 problem3
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…

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