Embedding and reconfiguration of spanning trees in faulty hypercubes

Abstract

The problem of tolerating faulty nodes in hypercubes has been studied by many researchers either by using spares or by reconfiguration. Algorithms for tolerating faulty nodes and links in hypercubes are presented. The algorithms are based on using general spanning trees (GST), complete unbalanced spanning trees (CUST), and balanced spanning trees (BST) for reconfiguring the hypercube to avoid faulty nodes and links. The algorithms contain 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 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. One hundred percent single fault correction (avoidance) and almost 100 percent fault correction (avoidance) of double and triple faults are achieved by the proposed algorithms for hypercubes having a dimension of n/spl ges/6. Simulation results for the algorithm under more than three faults also are presented. For any k faulty nodes (1/spl les/k/spl les/2/sup n/-1), the reconfiguration algorithm may be applied k times to avoid these k faulty nodes as long as no combination of any two of the faults results in a blocking situation. The proposed reconfiguration algorithms tolerate all possible single-link faults. The reconfiguration algorithms are extended to tolerate (k/spl les/n-1) multiple faults, causing blocking situation, with a backtracking.