  In the Constrained Fault-Tolerant Resource Allocation (FTRA) problem, we are
given a set of sites containing facilities as resources, and a set of clients
accessing these resources. Specifically, each site i is allowed to open at most
R_i facilities with cost f_i for each opened facility. Each client j requires
an allocation of r_j open facilities and connecting j to any facility at site i
incurs a connection cost c_ij. The goal is to minimize the total cost of this
resource allocation scenario.
  FTRA generalizes the Unconstrained Fault-Tolerant Resource Allocation
(FTRA_{\infty}) [18] and the classical Fault-Tolerant Facility Location (FTFL)
[13] problems: for every site i, FTRA_{\infty} does not have the constraint
R_i, whereas FTFL sets R_i=1. These problems are said to be uniform if all
r_j's are the same, and general otherwise.
  For the general metric FTRA, we first give an LP-rounding algorithm achieving
the approximation ratio of 4. Then we show the problem reduces to FTFL,
implying the ratio of 1.7245 from [3]. For the uniform FTRA, we provide a
1.52-approximation primal-dual algorithm in O(n^4) time, where n is the total
number of sites and clients. We also consider the Constrained Fault-Tolerant
k-Resource Allocation (k-FTRA) problem where additionally the total number of
facilities can be opened across all sites is bounded by k. For the uniform
k-FTRA, we give the first constant-factor approximation algorithm with a factor
of 4. Note that the above results carry over to FTRA_{\infty} and
k-FTRA_{\infty}.
