A Group-Theoretic Model for Symmetric Interconnection Networks
IEEE Transactions on Computers
An Orthogonal Multiprocessor for Parallel Scientific Computations
IEEE Transactions on Computers
Analysis and applications of the orthogonal access multiprocessor
Journal of Parallel and Distributed Computing
Analysis and Design of Parallel Algorithms: Arithmetic and Matrix Problems
Analysis and Design of Parallel Algorithms: Arithmetic and Matrix Problems
Orthogonal Graphs for the Construction of a Class of Interconnection Networks
IEEE Transactions on Parallel and Distributed Systems
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Orthogonal graphs are natural extensions of the classical binary and b-ary hypercubes b=2/sup l/ and are abstractions of interconnection schemes used for conflict-free orthogonal memory access in multiprocessor design. Based on the type of connection mode, these graphs are classified into two categories: those with disjoint and those with nondisjoint sets of modes. The former class coincides with the class of b-ary b=2/sup l/ hypercubes, and the latter denotes a new class of interconnection. It is shown that orthogonal graphs are Cayley graphs, a certain subgroup of the symmetric (permutation) group. Consequently these graphs are vertex symmetric, but it turns out that they are not edge symmetric. For an interesting subclass of orthogonal graphs with minimally nondisjoint set of modes, the shortest path routing algorithm and an enumeration of node disjoint (parallel) paths are provided. It is shown that while the number of node disjoint paths is equal to the degree, the distribution is not uniform with respect to Hamming distance as in the binary hypercube.