On the reconfigurability of embedded loops on hypercubes and its application

The topological structure and parallelism mechanism of hypercube interconnection make it attractive for parallel processing. Hypercubes with very large numbers of processors have been implemented. As the number of processors in a hypercube increases, the possibility of node failures also increases. This makes fault tolerance an important issue especially when hypercubes are to be used in applications requiring a high degree of dependability. Two approaches may be employed to incorporate fault tolerance into a hypercube: the first one uses redundant links and/or nodes to achieve fault tolerance; the second one uses reconfiguration algorithms to reallocate the tasks of failed nodes so that the computational structure of the interrupted parallel algorithm is preserved. In this paper, we use the second approach. The embedded computational structure here is a loop because many applications are implemented using loop structures. We propose a distributed reconfiguration algorithm for embedded loops and provide three fault-tolerant mapping schemes to facilitate the reconfiguration. The performance of these mappings is studied with respect to three measures: the average number of tolerable failures, the average number of task migrations, and the utilization rate of nodes. Finally, we apply the reconfiguration of loops to the reconfiguration of embedded multidimensional grids on hypercubes.