  We study popular local search and greedy algorithms for scheduling. The
performance guarantee of these algorithms is well understood, but the
worst-case lower bounds seem somewhat contrived and it is questionable if they
arise in practical applications. To find out how robust these bounds are, we
study the algorithms in the framework of smoothed analysis, in which instances
are subject to some degree of random noise.
  While the lower bounds for all scheduling variants with restricted machines
are rather robust, we find out that the bounds are fragile for unrestricted
machines. In particular, we show that the smoothed performance guarantee of the
jump and the lex-jump algorithm are (in contrast to the worst case) independent
of the number of machines. They are Theta(phi) and Theta(log(phi)),
respectively, where 1/phi is a parameter measuring the magnitude of the
perturbation. The latter immediately implies that also the smoothed price of
anarchy is Theta(log(phi)) for routing games on parallel links. Additionally we
show that for unrestricted machines also the greedy list scheduling algorithm
has an approximation guarantee of Theta(log(phi)).
