On the Fault Tolerance of Some Popular Bounded-Degree Networks

In this paper, we analyze the fault tolerance of several bounded-degree networks that are commonly used for parallel computation. Among other things, we show that an N-node butterfly network containing $N^{1-\epsilon}$ worst-case faults (for any constant $\epsilon 0$) can emulate a fault-free butterfly of the same size with only constant slowdown. The same result is proved for the shuffle-exchange network. 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. We also show that an N-node butterfly whose nodes fail with some constant probability p can emulate a fault-free network of the same type and size with a slowdown of 2O(log* N). These emulation schemes combine the technique of redundant computation with new algorithms for routing packets around faults in hypercubic networks. We also present techniques for tolerating faults that do not rely on redundant computation. These techniques tolerate fewer faults but are more widely applicable because they can be used with other networks such as binary trees and meshes of trees.