Multinode Broadcast in Hypercubes and Rings with Randomly Distributed Length of Packets

  • Authors:

  • E. A. Varvarigos;D. T. Bertsekas

  • Affiliations:

  • -;-

  • Venue:
  • IEEE Transactions on Parallel and Distributed Systems
  • Year:
  • 1993

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Abstract

Multinode broadcast (MNB) in a hypercube and in a ring network of processors isconsidered. It is assumed that the lengths of the packets that are broadcast are notfixed, but are distributed according to some probabilistic rule, and the optimal timesrequired to execute the MNB are compared for variable and for fixed packet lengths. Forlarge hypercubes, it is shown, under very general probabilistic assumptions on the packetlengths, that the MNB is completed in essentially the same time as when the packetlengths are fixed. In particular, the MNB is completed by time (1+ delta )T/sub s/ withprobability at least 1- epsilon , for any positive epsilon and delta , where T/sub s /is theoptimal time required to execute the MNB when the packet lengths are fixed at theirmean, provided that the size of the hypercube is large enough. In the case of the ring, itis proved that the average time required to execute a MNB when the packet lengths areexponentially distributed exceeds by a factor of ln n the corresponding time for the casethere the packet lengths are fixed at their mean, where n is the number of nodes of thering.