  Online models that allow recourse are highly effective in situations where
classical models are too pessimistic. One such problem is the online machine
covering problem on identical machines. In this setting, jobs arrive one by one
and must be assigned to machines with the objective of maximizing the minimum
machine load. When a job arrives, we are allowed to reassign some jobs as long
as their total size is (at most) proportional to the processing time of the
arriving job. The proportionality constant is called the migration factor of
the algorithm. Using a rounding procedure with useful structural properties for
online packing and covering problems, we design first a simple $(1.7 +
\varepsilon)$-competitive algorithm using a migration factor of
$O(1/\varepsilon)$ which maintains at every arrival a locally optimal solution
with respect to the Jump neighborhood. After that, we present as our main
contribution a more involved $(4/3+\varepsilon)$-competitive algorithm using a
migration factor of $\tilde{O}(1/\varepsilon^3)$. At every arrival, we run an
adaptation of the Largest Processing Time first (LPT) algorithm. Since the new
job can cause a complete change of the assignment of smaller jobs in both
cases, a low migration factor is achieved by carefully exploiting the highly
symmetric structure obtained by the rounding procedure.
