Weak Stable Matchings with Tenants and Ties

The paper addresses a variant of the stable marriage problem that models a job recruitment problem in which applicants are strictly ordered by priority but their preference lists may have ties. Some applicants may hold a post initially. These posts may be assigned to other applicants if their holders get another post. By reducing the problem to a sequence of maximum cardinality bipartite matching problems, combined with an effective propagation of the stability constraints, we show that applicant-optimal stable matchings may be found efficiently.