On Abelian Longest Common Factor with and without RLE
Abstract
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 runlength encoded and their compressed representations have size at most $m$. The alphabet size is denoted by $\sigma$. For the uncompressed problem, we show an $o(n^2)$time and $\Oh(n)$space algorithm in the case of $\sigma=\Oh(1)$, making a nontrivial use of tabulation. For the RLEcompressed problem, we show two algorithms: one working in $\Oh(m^2\sigma^2 \log^3 m)$ time and $\Oh(m (\sigma^2+\log^2 m))$ space, which employs line sweep, and one that works in $\Oh(m^3)$ time and $\Oh(m)$ space that applies in a careful way a slidingwindowbased approach. The latter improves upon the previously known $\Oh(nm^2)$time and $\Oh(m^4)$time algorithms that were recently developed by Sugimoto et al.\ (IWOCA 2017) and Grabowski (SPIRE 2017), respectively.
 Publication:

arXiv eprints
 Pub Date:
 April 2018
 arXiv:
 arXiv:1804.06809
 Bibcode:
 2018arXiv180406809G
 Keywords:

 Computer Science  Data Structures and Algorithms;
 68W32;
 F.2.2
 EPrint:
 Submitted to a journal