Talk:Polynomial-time approximation scheme

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Deleted statement

I deleted the following statement from the article:

"An important class of problems which have an FPRAS, but were thought until recently not to have a PTAS, is the class of #P-complete counting problems.^[1]"

I haven't read the reference, but it is definitely not true that all #P-complete problems have an FPRAS. This would, for instance, imply RP = NP. --Robin (talk) 13:24, 8 July 2009 (UTC)[reply]

Deleting that was the right thing to do but I just wanted to point out that we don't *know* that RP and NP are different so it's not correct to say that the statement you deleted is "definitely not true". It's just that most theoretical computer scientists (weasel, weasel) believe that NP and RP are *unlikely* to be the same, which means that it's *unlikely* that every #P-complete problem has an FPRAS. (Also, I've not read the cited article, either, but its title talks about FPTASes, not FPRASes.) Dricherby (talk) 15:06, 28 July 2009 (UTC)[reply]

You're right, but what I meant is its definitely not known to be true right now. I don't think the FPTAS/FPRAS distinction matters, because if you had an FPTAS to solve #P-complete problems that would imply something even stronger: P = NP. --Robin (talk) 17:23, 28 July 2009 (UTC)[reply]

References

^ Halman, Klabjan, Li, Orlin, Simchi-Levi, Fully polynomial time approximation schemes for stochastic dynamic programs, Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, 700–709, 2008.

PTAS completeness

What is meant by the statement "PTAS-reduction, L-reduction or P-reduction may be used to demonstrate PTAS-completeness"? I think that it does not make sense to define PTAS-completeness with respect to PTAS-reduction because then every problem in PTAS would be complete as one can reduce any other problem by choosing the error-parameter-dependent solution transformation g as the PTAS for the original problem, ignoring the solution of the transformed problem. This is the same issue as for P-completeness with respect to polynomial-time (many-one) reductions. --Maformatiker (talk) 18:04, 26 August 2016 (UTC)[reply]

[1] Halman, Klabjan, Li, Orlin, Simchi-Levi, Fully polynomial time approximation schemes for stochastic dynamic programs, Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms, 700–709, 2008.

[1]