Parallel processing subsystems with redundancy in a distributed environment

We consider the problem of dividing a-distributed system into subsystems for parallel processing, with redundancy for fault tolerance, where every subsystem has to consist),of at least three units. We prove that the problem of determining the maximum number of subsystems with redundancy for fault tolerance is NP-hard even in cubic planar 2-connected system topologies. We point out that this problem is APX-hard on cubic bipartite graphs. At last, for subcubic topologies without units connected to only one other unit, we give a linear time 4/3-approximation algorithm.