All-port total exchange in cartesian product networks

Authors:
Vassilios V. Dimakopoulos
Affiliations:
Department of Computer Science, University of Ioannia, P.O. Box 1186, GR-45110 Ioannina, Greece
Venue:
Journal of Parallel and Distributed Computing
Year:
2004

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Abstract

We present a general solution to the total exchange (TE) communication problem for any homogeneous multidimensional network under the all-port assumption. More specifically, we consider cartesian product networks where every dimension is the same graph (e.g. hypercubes, square meshes, n-ary d-cubes) and where each node is able to communicate simultaneously with all its neighbors. We show that if we are given an algorithm for a single n-node dimension which requires T steps, we can construct an algorithm for d-dimensions and running time of nd-1 T steps, which is provably optimal for many popular topologies. Our scheme, in effect, generalizes the TE algorithm given by Bertsekas et al. (J. Parallel Distrib. Comput. 11 (1991) 263-275) for the hypercubes and complements our theory (IEEE Trans. Parallel Distrib. Systems 9(7) (1998) 639) for the single-port model.