Fast Fault-Tolerant Resource Allocation

We present the first efficient approximation algorithm for the Unconstrained Fault-Tolerant Resource Allocation (UFTRA) problem [13] with uniform fault tolerance levels. UFTRA is a relaxation of the classical Fault-Tolerant Facility Location problem [11]. Based on the fundamental primal-dual theory [25], 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 [28] using a phase-greedy algorithm and improves the result of [29] adopting the linear program rounding technique. Built on this algorithm, we also show that the capacitated UFTRA (CUFTRA) problem introduced in [13] 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.