Editing Polynomial-time approximation scheme (section)

==As a complexity class==
The term PTAS may also be used to refer to the class of optimization problems that have a PTAS.  PTAS is a subset of [[APX]], and unless [[P = NP problem|P = NP]], it is a strict subset. <ref name=Jansen></ref>

Membership in PTAS can be shown using a [[PTAS reduction]], [[L-reduction]], or [[Approximation-preserving reduction#A-reduction and P-reduction|P-reduction]], all of which preserve PTAS membership, and these may also be used to demonstrate PTAS-completeness.  On the other hand, showing non-membership in PTAS (namely, the nonexistence of a PTAS), may be done by showing that the problem is APX-hard, after which the existence of a PTAS would show P = NP.  APX-hardness is commonly shown via PTAS reduction or [[Approximation-preserving reduction#AP-reduction|AP-reduction]].