A formal study on the fault tolerance of parallel and distributed systems

This paper analyzes the ability of several bounded degree networks that are commonly used for parallel computation to tolerate faults. Among other things it is shown that an N-node butterfly containing N^1-ε worst-case faults (for any constant ε>0) can emulate a fault-free butterfly of the same size with only constant slowdown. Similar results are proven for the shuffle-exchange graph. Hence, these networks become the first connected bounded-degree networks known to be able to sustain more than a constant number of worst-case faults without suffering more than a constant-factor slowdown in performance