Asymptotically Optimal Broadcasting and Gossiping in Faulty Hypercube Multicomputers

Various algorithms for reliable broadcasting (one-to-all) and gossiping (all-to-all) in faulty n-dimensional hypercube multicomputers are described and analyzed. For a broadcast (resp., a gossiping algorithm), the goal is that each processor receives complete information from the source (resp., from all the other processors) even in the presence of faults. One of the main characteristics of the proposed algorithms is that no information on the identity of the faulty nodes/links is required. Exchanges between processors are realized such that multiple copies of the same message move through disjoint paths. Solutions are proposed for systems which use a store-and-forward model of communication, the cost of the message transfer between two neighboring processors being modeled by the sum of a startup time plus a propagation time. Two cases are studied: (1) when processors can simultaneously communicate with all their neighbors at any time, and (2) when communications can take place with only one neighbor at a given time. The algorithms are asymptotically optimal. Optimal solutions for very short messages are also proposed. The speedup of these broadcasting algorithms over those designed for unitary length messages is about a factor of n. The gossiping algorithms require the minimum possible number of time steps and packet transmissions. >

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