An efficient implementation of the Gale and Shapley “propose-and-reject” algorithm

Abstract

We consider a version of the Hospitals/Residents problem which was first defined in 1962 by Gale and Shapley [9] under the name "College Admissions Problem". In particular, we consider the Firms/Candidates problem, where each Firm wishes to hire at least one Candidate and each Candidate can be finally assigned to a single Firm. We present an efficient implementation of the Gale and Shapley "propose-and-reject" algorithm when applied to the case of the Firms/Candidates problem.