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<p>We develop a characterization for m-fault-tolerant extensions, and for optimalm-fault-tolerant extensions, of a complete multipartite graph. Our formulation shows thatthis problem is equivalent to an interesting combinatorial problem on the partitioning ofintegers. This characterization leads to a new procedure for constructing an optimalm-fault-tolerant extension of any complete multipartite graph, for any m/spl ges/0. Theproposed procedure is mainly useful when the size of the graph is relatively small,because the search time required is exponential. This exponential search, however, is notalways necessary. We prove several necessary conditions that help us, in several cases,to identify some optimal m-fault-tolerant extensions without performing any search.</p>
Index Termsfault tolerant computing; fault-tolerant extension problem; complete multipartite networks; combinatorial problem; search time

A. A. Farrag and R. Dawson, "The Fault-Tolerant Extension Problem for Complete Multipartite Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 5, no. , pp. 205-210, 1994.
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