Stable matching is one of the oldest problems studied from an algorithmic point of view, whose original version is defined as follows: An instance consists of N men, N women, and each person’s preference list. A preference list is a totally ordered list including all members of the opposite sex depending on his/her preference. For a matching M between men and women, a pair of a man m and a woman w is called a blocking pair if both prefer each other to their current partners. A matching with no blocking pair is called stable
