Chapter 1

<Enter overview of chapter 1 here>

This section deals with the Stable Matching Problem, which was first posed by David Gale and Lloyd Shapely in 1962. This algorithm seeks to assign job applicants to potential employers in a way such that:

  "(i) Employers prefer every one of its accepted applicants to the remaining applicants; or \\
   (ii)Accepted job applicants prefer their current situation over working for other potential employers."

Either of these two options would result in a stable outcome to the problem.

To simplify this problem, Gale and Shapely made the assumption that every applicant sought a single employer, and every employer sought a single applicant. The latter, of course, would rarely be the case; however, the simplification allowed for the problem to be more easily defined while still maintaining the fundamental issues.