Why we cant have FPTAS for Strong NP complete problems

Question

I understood that we can apply FPTAS to the weak NP problems like 0-1 knapsack.

But why we cant apply the same principal to the strong NP problems like bin packing.I also checked wiki page about the same but understood very less.

This question belongs on http://programmers.stackexchange.com/ — tripleee, Oct 22 '13 at 06:07
This question appears to be off-topic because it is about theoretical computer science, which is more appropriate at cs.stackexchange.com. — templatetypedef, Nov 01 '13 at 02:36
@tripleee- Why does this belong on programmers? This is a CS theory question. — templatetypedef, Nov 01 '13 at 02:36

score 2 · Answer 1 · answered Nov 01 '13 at 17:50

If a stongly NP complete problem had an FPTAS, you could "trick" the approximation algorithm into giving an optimal solution. Details are here: http://www.idi.ntnu.no/~mlh/algkon/complexity.pdf

The existence of this FPTAS would give a polynomial time algorithm for NP-complete problem.

1 Answers1