Algorithms for ranking and unranking the combinatorial set of RNA secondary structures

01/27/2023

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by   Yuriy Shablya, et al.

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In this paper, we study the combinatorial set of RNA secondary structures of length n with m base-pairs. For a compact representation, we encode an RNA secondary structure by the corresponding Motzkin word. For this combinatorial set, we construct an AND/OR tree structure, find a bijection between the combinatorial set and the set of variants of the AND/OR tree, and develop algorithms for ranking and unranking the variants of the AND/OR tree. The developed ranking and unranking algorithms have polynomial time complexity O(m^2 (n - m)) for m < n - 2 m and O(m (n - m)^2) for m > n - 2 m. In contrast to the existing algorithms, the new algorithms do not require preprocessing steps and have better time complexity.