Complexity Analysis of Broadcasting in Hypercubes with Restricted Communication Capabilities

Abstract Typical algorithms for broadcasting in distributed memory multicomputers generally assume that the communication cost between two neighboring processors is one. A more elaborate model uses a sum of a start-up time and a propagation time which is proportional to the message length. This paper proposes a new model which incorporates into the cost function the number of communication links simultaneously used by each processor, and thus can also take into account the possibility of communicating in a restricted number of directions. Under these new hypotheses, we analyze and discuss the cost of broadcasting, gossiping, scattering, and multiscattering algorithms in n-dimensional hypercubes. In each case, a lower bound is computed, an asymptotically optimal algorithm is given, and efficient algorithms for short messages are described.

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