Sparse networks tolerating random faults for tree-like and butterfly-like networks

A network G* is called an RFT (random-fault-tolerant) network for a network G if G* contains a fault-free isomorphic copy of G with high probability even if processors fail independently with constant probability. This paper shows that if G is an N-processor partial k-tree, butterfly, wrapped butterfly, or Benes network then we can construct an RFT networks for G with O(N) processors and O(N log N) communication links.