# Understanding Popular Matchings via Stable Matchings

@article{Cseh2022UnderstandingPM, title={Understanding Popular Matchings via Stable Matchings}, author={{\'A}gnes Cseh and Yuri Faenza and Telikepalli Kavitha and Vladlena Powers}, journal={SIAM J. Discret. Math.}, year={2022}, volume={36}, pages={188-213} }

An instance of the marriage problem is given by a graph G together with, for each vertex of G, a strict preference order over its neighbors. A matching M of Gis popular in the marriage instance if M does not lose a head-to-head election against anymatching where vertices are voters. Every stable matching is a min-size popular matching; another subclass of popular matchings that always exist and can be easily computed is theset of dominant matchings. A popular matching M is dominant if M wins…

## Figures from this paper

## 4 Citations

### Maximum-utility popular matchings with bounded instability

- MathematicsArXiv
- 2022

. In a graph where vertices have preferences over their neighbors, a matching is called popular if it does not lose a head-to-head election against any other matching when the vertices vote between…

### Maximum Matchings and Popularity

- Computer Science, EconomicsICALP
- 2021

Here it is shown that when there are edge costs, a min-cost popular max-matching in $G$ can be computed in polynomial time, in contrast to the min- cost popular matching problem which is known to be NP-hard.

### Quasi-popular Matchings, Optimality, and Extended Formulations

- MathematicsSODA
- 2020

This version of the paper goes beyond the conference version in the following two points: (i) the algorithm for finding a quasi-popular matching of cost at most that of a min-cost popular fractional matching is new; (ii) the proofs from Section 6.3 are now self-contained.

### Popular Critical Matchings in the Many-to-Many Setting

- MathematicsArXiv
- 2022

. We consider the many-to-many bipartite matching problem in the presence of two-sided preferences and two-sided lower quotas. The input to our problem is a bipartite graph G = ( A ∪ B , E ), where…

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