Paper ID: 5832
The structure of stable marriage with indifference
Discrete Applied Mathematics, volume 122
Page Numbers : 167-181
Publisher: Elsevier Science
URL: This publication is available at this URL.
We consider the stable marriage problem where participants are permitted to express indifference in their preference lists (i.e., each list can be partially ordered). We prove that, in an instance where indifference takes the form of ties, the set of strongly stable matchings forms a distributive lattice. However, we show that this lattice structure may be absent if indifference is in the form of arbitrary partial orders. Also, for a given stable marriage instance with ties, we characterise strongly stable matchings in terms of perfect matchings in bipartite graphs. Finally, we briefly outline an alternative proof of the known result that, in a stable marriage instance with indifference in the form of arbitrary partial orders, the set of super-stable matchings forms a distributive lattice.
Keywords: Stable marriage problem; Partial order; Tie; Strong stability; Super-stability