Constrained Fault-Tolerant Resource Allocation

We follow [18,25] and give a series of improved results for the Constrained Fault-Tolerant Resource Allocation (FTRA) problem. In FTRA, we are given a set of sites containing facilities as resources, and a set of clients consuming these resources. Specifically, each site i is allowed to open at most Ri facilities with cost fi for each opened facility. Each client j requires an allocation of rj facilities and connecting j to any facility at site i incurs a connection cost cij . The goal is to minimize the total cost of this resource allocation scenario. FTRA generalizes the Unconstrained Fault-Tolerant Resource Allocation (FTRA∞) [18] and the classical Fault-Tolerant Facility Location (FTFL) [13] problems: for every site i, FTRA∞ does not have the constraint Ri, whereas FTFL sets Ri = 1. These problems are said to be uniform if all rj ’s are the same, and general otherwise. In this paper, we strive to close the gap between FTRA and FTFL from the perspective of approximation. For the general metric FTRA, we first give an LP-rounding algorithm achieving the approximation ratio of 4. Then we show its reduction to FTFL, implying the ratio of 1.7245. For the uniform FTRA, we provide a 1.52-approximation primal-dual algorithm in O ( n ) , where n is the total number of sites and clients. For completeness in the line of [25] for FTFL, we also consider the Constrained Fault-Tolerant k-Resource Allocation (KFTRA) problem where additionally the total number of facilities can be opened across the sites is at most k. For the uniform KFTRA, we give the first constantfactor approximation algorithm with a factor of 4. Note that the above results carry over to FTRA∞ and KFTRA∞.