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

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