On the Conversion between Binary Code and Binary-Reflected Gray Code on Boolean Cubes

نویسندگان

Lennart Johnsson

Ching-Tien Ho

چکیده

We present a new algorithm for conversion between binary code and binary{re ected Gray code that requires approximately 2K 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 K 2 + 1 element transfers, which is optimal. The new algorithm is optimal within a factor of 1 3 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 K with concurrent communication on all channels of every node of a binary cube.

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