Abstract
The suffix array \( SA _{w}\) of a string w of length n is a permutation of [1..n] such that \( SA _{w}[i] = j\) iff w[j, n] is the lexicographically i-th suffix of w. In this paper, we consider variants of the reverse-engineering problem on suffix arrays with two given permutations P and Q of [1..n], such that P refers to the forward suffix array of some string w and Q refers to the backward suffix array of the reversed string \(w^R\). Our results are the following: (1) An algorithm which computes a solution string over an alphabet of the smallest size, in O(n) time. (2) The exact number of solution strings over an alphabet of size \(\sigma \). (3) An efficient algorithm which computes all solution strings in the lexicographical order, in time near optimal up to \(\log n\) factor.
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Acknowledgements
This work was supported by JSPS KAKENHI Grant Numbers JP18K18002 (YN), JP17H01697 (SI), JP16H02783 (HB), and JP18H04098 (MT).
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Kuhara, Y., Nakashima, Y., Inenaga, S., Bannai, H., Takeda, M. (2018). Recovering, Counting and Enumerating Strings from Forward and Backward Suffix Arrays. In: Gagie, T., Moffat, A., Navarro, G., Cuadros-Vargas, E. (eds) String Processing and Information Retrieval. SPIRE 2018. Lecture Notes in Computer Science(), vol 11147. Springer, Cham. https://doi.org/10.1007/978-3-030-00479-8_21
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