  We consider the online problem of minimizing weighted flow-time on unrelated
machines. Although much is known about this problem in the
resource-augmentation setting, these results assume that jobs can be preempted.
We give the first constant-competitive algorithm for the non-preemptive setting
in the rejection model. In this rejection model, we are allowed to reject an
$\varepsilon$-fraction of the total weight of jobs, and compare the resulting
flow-time to that of the offline optimum which is required to schedule all
jobs. This is arguably the weakest assumption in which such a result is known
for weighted flow-time on unrelated machines. While our algorithms are simple,
we need a delicate dual-fitting argument to bound the flow-time while only a
small fraction of elements are rejected.
