Saturating stable matchings

Stable Matchings

Stable Schedule Matchings

In order to treat a natural schedule matching problem related with worker-firm matchings, we generalize some theorems of Baiou–Balinski and Alkan–Gale by applying a fixed point method of Fleiner.

Conditional Stable Matchings

In matching theory of contracts the substitutes condition plays an essential role to ensure the existence of stable matchings. We study manyto-many matchings where groups of individuals, of size possibly greater than two, are matched to a set of institutions. Real-world examples include orphan brothers accepting an adoptive family conditional on all of them being included; hiring contracts that...

Socially Stable Matchings

In two-sided matching markets, the agents are partitioned into two sets. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their assigned matches. In this paper we study a variant of stable matching motivated by the fact that...

Stable Matchings in Trees

The maximum stable matching problem (Max-SMP) and the minimum stable matching problem (Min-SMP) have been known to be NP-hard for subcubic bipartite graphs, while Max-SMP can be solved in polynomal time for a bipartite graph G with a bipartition (X,Y ) such that degG(v) ≤ 2 for any v ∈ X. This paper shows that both Max-SMP and Min-SMP can be solved in linear time for trees. This is the first po...