Partial Multinode Broadcast Algorithms for D-Dimensional Meshes

In this paper we consider the partial multinode broadcast and the partial exchange communication tasks in d-dimensional meshes. The partial multinode broadcast in an N-processor network is the task in which each of M < N arbitrary nodes broadcast a packet to all the remaining N 1 nodes. Correspondingly, in the partial exchange there are M < N nodes that wish to send a separate, personalized packet to each of the other nodes. We propose algorithms for the d-dimensional mesh network that execute the partial multinode broadcast and the partial exchange communication tasks in near-optimal time. No assumption concerning the location of the M source nodes is made. The communication algorithms proposed are "on line" and distributed. We further look at a dynamic version of the problem, where broadcast requests are generated at random times. In particular, we assume that the broadcast requests are generated at each node of the mesh according to a Poisson distribution with rate A. Based on the partial multinode broadcast algorithm, we propose a dynamic decentralized scheme to execute the broadcasts in this dynamic environment. We find an upper bound on the average delay required to serve each broadcast. We prove that the algorithm is stable for network utilization p close to 1, and the average delay is of the order of the diameter for any load in the stability region. 1 Research supported by NSF under Grant NSF-DDM-8903385 and by the ARO under Grant DAAL03-86K-0171. 2 Laboratory for Information and Decision Systems, M.I.T, Cambridge, Mass. 02139.