We present the first efficient approximation algorithm for the Unconstrained Fault-Tolerant Resource Allocation (UFTRA) problem  with uniform fault tolerance levels. UFTRA is a relaxation of the classical Fault-Tolerant Facility Location problem . Based on the fundamental primal-dual theory , our primal-dual algorithm achieves an approximation ratio of 1.861 while it can be implemented in quasi-linear time. Besides the significant improvement in runtime over all previous work, the solution quality of the algorithm matches the work in  using a phase-greedy algorithm and improves the result of  adopting the linear program rounding technique. Built on this algorithm, we also show that the capacitated UFTRA (CUFTRA) problem introduced in  achieves 3.722- approximation in quasi-linear time. In this paper, before the presence of the main algorithm and its extensive theoretical analysis, we provide some necessary background knowledge of the problem. This includes the problem's mathematical model formulation, the primal-dual theory applied to this formulation, and the problem's abstract system model with its potential application domains such as content distribution networks and cloud computing.