Roth-Peranson algorithm

The Roth-Peranson algorithm is a computerized method used to match applicants (like medical residents) to programs (like hospitals). It works by having programs and applicants submit preferences, and then iteratively proposing and re-proposing matches to find a stable, mutually satisfactory arrangement. The algorithm ensures that no applicant and program would prefer to be matched with each other over their current match, leading to a fair, optimal outcome for both sides. It is designed to efficiently produce stable matches in complex matching systems, similar to the way the stable marriage problem is solved.