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On the conversion between binary code and binary-reflected Gray code on binary cubes

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2 Author(s)
Johnsson, S.L. ; Dept. of Comput. Sci., Harvard Univ., Cambridge, MA, USA ; Ching-Tien Ho

We present a new algorithm for conversion between binary code and binary-reflected Gray code that requires approximately 2 K/3 element transfers in sequence for K elements per node, compared to K element transfers for previously known algorithms. For a binary cube of n=2 dimensions the new algorithm degenerates to yield a complexity of 2 K/+1 element a transfers, which is optimal. The new algorithm is optimal to within a multiplicative factor of 4/3 with respect to the best known 3 lower bound for any routing strategy. We show that the minimum number of element transfers for minimum path length routing is K with concurrent communication on all channels of every node of a binary cube

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Computers, IEEE Transactions on  (Volume:44 ,  Issue: 1 )