For any integer n ≥ 1 a middle levels Gray code is a cyclic listing of all bitstrings of length 2n+1 that have either n or n+1 entries equal to 1 such that any two consecutive bitstrings in the list differ in exactly one bit. The question whether such a Gray code exists for every n ≥ 1 has been the subject of intensive research during the last 30 years, and has been answered affirmatively only recently [T. Mütze. Proof of the middle levels conjecture. arXiv:1404.4442, 2014]. In this work we provide the first efficient algorithm to compute a middle levels Gray code. For a given bitstring, our algorithm computes the next ℓ bitstrings in the Gray code in time [Formula presented], which is O(n) on average per bitstring provided that ℓ = Ω(n).
CITATION STYLE
Mütze, T., & Nummenpalo, J. (2015). Efficient computation of middle levels gray codes. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9294, pp. 915–927). Springer Verlag. https://doi.org/10.1007/978-3-662-48350-3_76
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