Abstract
Two strings are considered Abelian equivalent if one is a permutation of the other. We deal with two problems from Abelian stringology: computing regular Abelian periods of a given string and computing the longest common Abelian factor (LCAF) of two given strings. For the former problem our solution works in \(O(n\log m)\) time, where m is the length of the run-length encoded string, which improves the O(nm)-time result from [5]. For LCAF we propose two solutions, one working in \(O(n+m^4)\) time and O(n) space, the other requiring \(O(n^{3/2}\sigma \sqrt{m\log n})\) time and \(O(n\sigma )\) space (for \(m = O(n / \log n)\)).
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Notes
- 1.
More precisely, their lemma allows to check in constant time if two prefixes of the given string w have proportional Parikh vectors, assuming that both prefixes contain all symbols from the alphabet for w. In our setting, in \(O(n\log \sigma )\) time we can compute the maximum q over the first positions of each alphabet symbol in S, and if \(j < q\), then j cannot be a period of S and is immediately discarded.
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Grabowski, S. (2017). Regular Abelian Periods and Longest Common Abelian Factors on Run-Length Encoded Strings. In: Fici, G., Sciortino, M., Venturini, R. (eds) String Processing and Information Retrieval. SPIRE 2017. Lecture Notes in Computer Science(), vol 10508. Springer, Cham. https://doi.org/10.1007/978-3-319-67428-5_17
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DOI: https://doi.org/10.1007/978-3-319-67428-5_17
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