In the stable matching problem introduced by Gale and Shapley, it is known that in the case where the preference lists may involve ties, a stable matching always exists, but the sizes of stable matchings may be different. In this paper, we consider the problem of finding a maximum-size stable matching in a many-to-many matching market with ties. It is known that this problem is NP-hard even if the capacity of every agent is one. In this paper, we prove that this problem in trees can be solved in polynomial time by extending the algorithm proposed by Tayu and Ueno for the one-to-one setting.
|Number of pages||16|
|Journal||Journal of the Operations Research Society of Japan|
|Publication status||Published - Jan 1 2016|
All Science Journal Classification (ASJC) codes
- Decision Sciences(all)
- Management Science and Operations Research