  In this paper we study the classical no-wait flowshop scheduling problem with
makespan objective (F|no-wait|C_max in the standard three-field notation). This
problem is well-known to be a special case of the asymmetric traveling salesman
problem (ATSP) and as such has an approximation algorithm with logarithmic
performance guarantee. In this work we show a reverse connection, we show that
any polynomial time \alpha-approximation algorithm for the no-wait flowshop
scheduling problem with makespan objective implies the existence of a
polynomial-time \alpha(1+\epsilon)-approximation algorithm for the ATSP, for
any \epsilon>0. This in turn implies that all non-approximability results for
the ATSP (current or future) will carry over to its special case. In
particular, it follows that no-wait flowshop problem is APX-hard, which is the
first non-approximability result for this problem.
