Mixed fault tolerance in server assignment: Combining reinforcement and backup

We study the mixed approach to fault tolerance in the general context of server assignment in networks. The approach is based on mixing two different existing strategies, namely, reinforcement and backup. The former strategy protects clients by reinforcing the servers assigned to them and making them fault-resistant, possibly at a high cost, while the latter protects clients by assigning to them alternate low price backup servers that can replace their primary servers in case those fail. Applying the mixed approach to fault tolerance gives rise to new fault tolerant variations of known server assignment problems. We introduce several NP-hard problems of this type, including the mixed fault-tolerant dominating set problem, the mixed fault-tolerant centers problem, and the mixed fault-tolerant facility location problem, and present polynomial time approximation algorithms for them, demonstrating the viability of the mixed strategy for server assignment problems.