Regular Abelian Periods and Longest Common Abelian Factors on Run-Length Encoded Strings

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 $m = O(n / \log n)$).