On designing fault-tolerant extensions with optimal fanout for complete bipartite networks
A major goal in designing multicomputer networks is to include fault-tolerance capability so that the system can continue to operate correctly after losing some of its basic components. This is normally achieved by introducing redundancy, that is, by including spare nodes (processors) and extra edges (links). It is desirable that these extra nodes and edges be minimized to reduce the cost of tolerating failure. This approach, however, tend to distribute the edges unevenly over the nodes. Thus, it can lead to solutions with maximal fanout, which may not be acceptable in practice. In this paper, we propose an alternate approach in which minimizing fanout has higher priority over minimizing edges. We apply this approach to the problem of constructing k-fault-tolerant (k-ft) extensions of complete bipartite networks, where k is the number of nodes failure to be tolerated. For arbitrary values of k, our results indicate that finding a fanout-optimal solution is very difficult, and might require an exponential search. The algorithm proposed for finding such an optimal solution, for any k, is useful only when the size of the network is not very large. For small values of k, (e.g., k=1), we show that an optimal solution can be constructed in polynomial time.
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