Abstract
A string S of length n has period P of length p if \(S[i]=S[i+p]\) for all \(1 \le i \le n-p\) and \(n \ge 2p\). The shortest such substring, P, is called the period of S, and the string S is called periodic in P. In this paper we investigate the period recovery problem. Given a string S of length n, find the primitive period(s) P such that the distance between S and the string that is periodic in P is below a threshold \(\tau \). We consider the period recovery problem over both the Hamming distance and the edit distance. For the Hamming distance case, we present an \(O(n \log n)\) time algorithm, where \(\tau \) is given as \(\frac{n}{(2+\epsilon )p}\), for \(0 < \epsilon < 1\). For the edit distance case, \(\tau =\frac{n}{(4+\epsilon )p}\), and we provide an \(O(n^{4/ 3})\) time algorithm.
A. Amir—Partially supported by the Israel Science Foundation grant 571/14, and grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF).
M. Amit—Partially supported by the Israel Science Foundation grant 571/14, grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF) and DFG.
G. M. Landau—Partially supported by the Israel Science Foundation grant 571/14, grant No. 2014028 from the United States-Israel Binational Science Foundation (BSF) and DFG.
D. Sokol—Partially supported by the United States-Israel Binational Science Foundation (BSF) grant No. 2014028.
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In previous work, the lemmas state “up to cyclic rotations” which means that one conjugate is counted/reported for each set of cyclic permutations of a given period P. Here we clarify this language by always finding the single best conjugate.
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Amir, A., Amit, M., Landau, G.M., Sokol, D. (2016). Period Recovery over the Hamming and Edit Distances. In: Kranakis, E., Navarro, G., Chávez, E. (eds) LATIN 2016: Theoretical Informatics. LATIN 2016. Lecture Notes in Computer Science(), vol 9644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49529-2_5
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