An application of Minimum Cut theorem
Cees Elzinga, Sven Rahmann and Hui Wang have perfectly explained several algorithms on string sequences on their paper , namely Algorithms for Subsequence Combinatorics.
In order to understard the algorithm better, I prepared a visual representation of the algorithm steps in this powerpoint file. It may be a helpful visual guide for those who are struggling with the details of the algorithms. I would like to, also, take this opportunity to thank each and everyone of the authors of the paper.