Research problems: problem 109 (posed by Peter J. Slater)
Discrete Mathematics
Introduction to parallel algorithms and architectures: array, trees, hypercubes
Introduction to parallel algorithms and architectures: array, trees, hypercubes
A Survey of Combinatorial Gray Codes
SIAM Review
Discrete Mathematics - Kleitman and combinatorics: a celebration
The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations (Art of Computer Programming)
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An n-bit (cyclic) Gray code is a (cyclic) ordering of all n-bit strings such that consecutive strings differ in exactly one bit. We construct an n-bit cyclic Gray code C"n whose graph of transitions is isomorphic to an induced subgraph of the d-dimensional hypercube where d=@?lgn@?. This allows to represent C"n so that only @Q(loglogn) bits per n-bit string are needed. We provide an explicit description of an algorithm which generates the transition sequence of C"n in linear time with respect to the output size.