Maximum-utility Popular Matchings with Bounded Instability

Schlotter, Ildikó Anna and Cseh, Ágnes (2025) Maximum-utility Popular Matchings with Bounded Instability. ACM TRANSACTIONS ON COMPUTATION THEORY, 17 (1). No.-6. ISSN 1942-3454

Text unstable-pop-toct.pdf - Published Version Restricted to Repository staff only Download (641kB) | Request a copy

Abstract

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.

Actions (login required)

Edit Item