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<p><b>Abstract</b>—We develop a formal and systematic methodology for designing an optimal multiple bus system (MBS) realizing a set of interconnection functions whose graphical representation (denoted as IFG) is symmetric. The problem of constructing an optimal MBS for a given IFG is NP-Hard. In this paper, we show that polynomial time solutions exist when the IFG is vertex symmetric. This is the case of interest for the vast majority of important interconnection function sets.</p><p>We present a particular partition (which can be found in polynomial time) on the edge set of a vertex symmetric IFG, that produces a symmetric MBS with minimum number of buses as well as minimum number of interfaces. We demonstrate several advantages of such an MBS over a direct-link architecture realizing the same IFG, in terms of the number of ports per processor, number of neighbors per processors, and the diameter.</p>
Bus minimization, Cayley color graph, interconnection function, interconnection network, interface minimization, multiple bus system, optimal design, SIMD operation.

A. El-Amawy and P. Kulasinghe, "Optimal Realization of Sets of Interconnection Functions on Synchronous Multiple Bus Systems," in IEEE Transactions on Computers, vol. 45, no. , pp. 964-969, 1996.
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