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arXiv · 2003.03222

Generating a Gray code for prefix normal words in amortized polylogarithmic time per word

Péter Burcsi·Gabriele Fici·Zsuzsanna Lipták·Rajeev Raman·Joe Sawada
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Abstract

A prefix normal word is a binary word with the property that no substring has more $1$s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal words of length $n$ as a combinatorial Gray code, where successive strings differ by at most two swaps or bit flips. This Gray code can be generated in $\Oh(\log^2 n)$ amortized time per word, while the best generation algorithm hitherto has $\Oh(n)$ running time per word. We also present a membership tester for prefix normal words, as well as a novel characterization of bubble languages.

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Péter Burcsi, Gabriele Fici, Zsuzsanna Lipták, Rajeev Raman, Joe Sawada. 2020-03-05. Generating a Gray code for prefix normal words in amortized polylogarithmic time per word. https://doi.org/10.1016/j.tcs.2020.07.035

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