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<p>We present a new algorithm for conversion between binary code and binary-reflected Gray code that requires approximately <math><tmath>\scriptstyle{2K \over 3}</tmath></math> element transfers in sequence for <it>K</it> elements per node, compared to <it>K</it> element transfers for previously known algorithms. For a binary cube of <math><tmath>n = 2</tmath></math> dimensions the new algorithm degenerates to yield a complexity of <math><tmath>{K \over 2} + 1</tmath></math> element transfers, which is optimal. The new algorithm is optimal to within a multiplicative factor of <math><tmath>\scriptstyle{4\over 3}</tmath></math> with respect to the best known lower bound for any routing strategy. We show that the minimum number of element transfers for minimum path length routing is <math><tmath>{K}</tmath></math> with concurrent communication on all channels of every node of a binary cube.</p>
Gray-to-binary conversion, binary code encoding, Gray code encoding, hypercubes, permutation, routing algorithm, communication algorithm, all-port communication.
Ching-Tien Ho, S. Lennart Johnsson, "On the Conversion Between Binary Code and Binary-Reflected Gray Code on Binary Cubes", IEEE Transactions on Computers, vol. 44, no. , pp. 47-53, January 1995, doi:10.1109/12.368010
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