A distributed approximation algorithm for fault-tolerant metric facility location

In this paper, we propose an approximation algorithm for the Fault-Tolerant Metric Facility Location problem which can be implemented in a distributed and asynchronous manner within O(n) rounds of communication, where n is the number of vertices in the network. Given a constant size set $\mathcal{R} $ which represents distinct levels of fault-tolerant requirements of all cities, as well as the two-part (facility and connection) cost of the optimal solution, i.e. F* + C*, the cost of our solution is no more than $|\mathcal{R}|\, \cdot \,F^* \, + \,2C^* $ for the general case, and less than F* + 2C* for the special case where all cities have a uniform connectivity requirement. Extensive numerical experiments showed that the quality of our solutions is comparable (within 4% error) to the optimal solution in practice.