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Issue No.01 - January (1995 vol.44)
pp: 47-53
ABSTRACT
<p>We present a new algorithm for conversion between binary code and binary-reflected Gray code that requires approximately $<tmath>\scriptstyle{2K \over 3}</tmath>$ 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 $<tmath>n = 2</tmath>$ dimensions the new algorithm degenerates to yield a complexity of $<tmath>{K \over 2} + 1</tmath>$ element transfers, which is optimal. The new algorithm is optimal to within a multiplicative factor of $<tmath>\scriptstyle{4\over 3}</tmath>$ 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 $<tmath>{K}</tmath>$ with concurrent communication on all channels of every node of a binary cube.</p>
INDEX TERMS
Gray-to-binary conversion, binary code encoding, Gray code encoding, hypercubes, permutation, routing algorithm, communication algorithm, all-port communication.
CITATION
S. Lennart Johnsson, Ching-Tien Ho, "On the Conversion Between Binary Code and Binary-Reflected Gray Code on Binary Cubes", IEEE Transactions on Computers, vol.44, no. 1, pp. 47-53, January 1995, doi:10.1109/12.368010