Several researchers have analysed the performance of k-ary n-cubes taking into account channel bandwidth constraints imposed by implementation technology, namely the constant wiring density and pin-out constraints for VLSI and multiple-chip technology respectively. For instance, Dally [IEEE Trans. Comput. 39(6) (1990) 775], Abraham [Issues in the architecture of direct interconnection networks schemes for multiprocessors, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1992], and Agrawal [IEEE Trans. Parallel Distributed Syst. 2(4) (1991) 398] have shown that low-dimensional k-ary n-cubes (known as tori) outperform their high-dimensional counterparts (known as hypercubes) under the constant wiring density constraint. However, Abraham and Agrawal have arrived at an opposite conclusion when they considered the constant pin-out constraint. Most of these analyses have assumed deterministic routing, where a message always uses the same network path between a given pair of nodes. More recent multicomputers have incorporated adaptive routing to improve performance. This paper re-examines the relative performance merits of the torus and hypercube in the context of adaptive routing. Our analysis reveals that the torus manages to exploit its wider channels under light traffic. As traffic increases, however, the hypercube can provide better performance than the torus. Our conclusion under the constant wiring density constraint is different from that of the works mentioned above because adaptive routing enables the hypercube to exploit its richer connectivity to reduce message blocking.
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