Embedding general spanning trees in faulty hypercubes
The problem of tolerating faulty nodes in hypercubes has been studied by many researchers either by using spares or by reconfiguration. in this paper, an algorithm for tolerating faulty nodes in hypercubes is presented. The algorithm is based on using general spanning trees for reconfiguring the hypercube to avoid faulty nodes. The algorithm contains two phases: the first phase involves the construction of the spanning tree, and the second one is for reconfiguring the hypercube should a faulty node be detected. The reconfiguration process introduced consists of two basic steps. First, the faulty node is disconnected from the spanning tree. Then, a new spanning tree is constructed by reconnecting the children of the faulty node to the spanning tree. This paper deals with reconfiguring faulty hypercubes; however, the same algorithm can be generalized to work for reconfiguration of multicomputer networks in general in the presence of faults. Single fault coverage of 100% and almost 100% fault coverage of double and triple faults are achieved by the proposed algorithm, with no dilation for hypercubes having a dimension of n greater than or equal to 10. Simulation results for the algorithm under more than three faults also are presented. Fault coverage and congestion results for up to 60 faults having different cube sizes are discussed.
spanning trees faulty hypercubes reconfiguration dilation fault tolerance