at Google ScholarTitle data
Schlotter, Ildiko ; Cseh, Ágnes:
Maximum-utility Popular Matchings with Bounded Instability.
In: ACM Transactions on Computation Theory.
Vol. 17
(8 March 2025)
Issue 1
.
ISSN 1942-3462
DOI: https://doi.org/10.1145/3711843
Abstract in another language
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 the matchings. Popular matchings can be seen as an intermediate category between stable matchings and maximum-size matchings. In this article, we aim to maximize the utility of a matching that is popular but admits only a few blocking edges.We observe that, for general graphs, finding a popular matching with at most one blocking edge is already NP-complete. For bipartite instances, we study the problem of finding a maximum-utility popular matching with a bound on the number (or, more generally, the cost) of blocking edges applying a multivariate approach. We show classical and parameterized hardness results for severely restricted instances. By contrast, we design an algorithm for instances where preferences on one side admit a master list and show that this algorithm is roughly optimal.
Further data
| Item Type: | Article in a journal |
|---|---|
| Refereed: | Yes |
| Keywords: | Popular matching; stable matching; complexity; master lists |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics > Chair Mathematical Economics - Univ.-Prof. Dr. Jörg Rambau Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Dynamical Systems and Data > Chair Dynamical Systems and Data - Univ.-Prof. Dr. Peter Koltai |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |
| Date Deposited: | 12 Mar 2025 11:47 |
| Last Modified: | 12 Mar 2025 11:47 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/92780 |