So, a quick search on the web led me to believe that "APXHardness implies that no QPTAS exist for a problem unless [some complexity class] is included in some [other complexity class]" and it is well known too! It seems like everybody knows this except for me. Unfortunately, no reference to support this statement is given. I have two questions:
What is the strongest version of this statement that is currently known?
A reference? Please?
Thanks in advance.
Chandra Chekuri's answer suggests that a $QPTAS$ for a $APX$-hard problem implies $NP\subseteq QP$. Can anyone explain why it is true, or preferably give a reference for that? In other words, why does quasi polynomial time approximability imply QP time solvability?