Problems related to data placement and replication are of fundamental interest
both in the area of large scale distributed networking systems as well as
centralized storage systems. In this work, we consider several variants of a
basic resource replication, and propose new approximation results for them. We
observe that the threshold graph technique, which has been applied to several
$k$-center
type problems, yields simple and efficient approximation algorithms for
resource replication problems. Our results range from positive (efficient,
small constant factor, approximation algorithms) to extremely negative
(impossibility of existence of any algorithm with non-trivial approximation
guarantee, i.e., with positive approximation ratio) for different versions of
the problem.