Sparse Networks Tolerating Random Faults

A network G∗ is called random-fault-tolerant (RFT) network for a network G if G∗ contains a fault-free isomorphic copy of G with high probability even if each processor fails independently with constant probability. This paper proposes a general method to construct an RFT network G∗ for any network G with N processors such that G∗ has O(N ) processors. Based on the construction, we also show that if G is a Cayley, de Bruijn, shu7e-exchange, or partial k-tree network with N processors and M communication links then we can construct an RFT network for G with O(N ) processors and O(M logN ) communication links. Cayley networks contain many popular networks such as circulant, hypercube, CCC, wrapped butter9y, star, and pancake networks. ? 2003 Elsevier B.V. All rights reserved.