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Orthogonal Graphs for the Construction of a Class of Interconnection Networks
January 1991 (vol. 2 no. 1)
pp. 3-19

A graph theoretical representation for a class of interconnection networks is suggested.The idea is based on a definition of orthogonal binary vectors and leads to a constructionrule for a class of orthogonal graphs. An orthogonal graph is first defined as a set of2/sup m/ nodes, which in turn are linked by 2/sup m-n/ edges for every link model definedin an integer set Q*. The degree and diameter of an orthogonal graph are determined interms of the parameters n, m, and the number of link modes defined in Q*. Routing inorthogonal graphs is shown to reduce to the node covering problem in bipartite graphs.The proposed theory is applied to describe a number of well-known interconnectionnetworks such as the binary m-cube and spanning-bus meshes. Multidimensional access (MDA) memories are also shown as examples of orthogonal shared memory multiprocessingsystems. Finally, orthogonal graphs are applied to the construction of multistageinterconnection networks. Connectivity and placement rules are given and shown to yielda number of well-known networks.

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Index Terms:
multidimensional access memories; connectivity; graph theoretical representation;interconnection networks; orthogonal binary vectors; link modes; node covering problem;bipartite graphs; binary m-cube; spanning-bus meshes; orthogonal shared memorymultiprocessing systems; placement; graph theory; multiprocessor interconnectionnetworks
I.D. Scherson, "Orthogonal Graphs for the Construction of a Class of Interconnection Networks," IEEE Transactions on Parallel and Distributed Systems, vol. 2, no. 1, pp. 3-19, Jan. 1991, doi:10.1109/71.80185
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