On Abelian Longest Common Factor with and without RLE
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We consider the Abelian longest common factor problem in two scenarios: when input strings are uncompressed and are of size n, and when the input strings are run-length encoded and their compressed representations have size at most m. The alphabet size is denoted by σ. For the uncompressed problem, we show an o(n^2)-time and (n)-space algorithm in the case of σ=(1), making a non-trivial use of tabulation. For the RLE-compressed problem, we show two algorithms: one working in (m^2σ^2 ^3 m) time and (m (σ^2+^2 m)) space, which employs line sweep, and one that works in (m^3) time and (m) space that applies in a careful way a sliding-window-based approach. The latter improves upon the previously known (nm^2)-time and (m^4)-time algorithms that were recently developed by Sugimoto et al. (IWOCA 2017) and Grabowski (SPIRE 2017), respectively.
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