Popular mixed matchings

Popular Mixed Matchings

We study the problem of matching applicants to jobs under one-sided preferences; that is, each applicant ranks a non-empty subset of jobs under an order of preference, possibly involving ties. A matching M is said to be more popular than T if the applicants that prefer M to T outnumber those that prefer T to M . A matching is said to be popular if there is no matching more popular than it. Equi...

Popular Matchings

Optimal popular matchings

In this paper we consider the problem of computing an ‘‘optimal’’ popular matching. We assume that our input instance G = (A∪P , E1 ∪̇ · · · ∪̇ Er ) admits a popular matching and here we are asked to return not any popular matching but an optimal popular matching, where the definition of optimality is given as a part of the problem statement; for instance, optimality could be fairness inwhich cas...

Maintaining Near-Popular Matchings

We study dynamic matching problems in graphs among agents with preferences. Agents and/or edges of the graph arrive and depart iteratively over time. The goal is to maintain matchings that are favorable to the agent population and stable over time. More formally, we strive to keep a small unpopularity factor by making only a small amortized number of changes to the matching per round. Our main ...

Popular Half-Integral Matchings

In an instance G = (A∪B,E) of the stable marriage problem with strict and possibly incomplete preference lists, a matchingM is popular if there is no matchingM ′ where the vertices that prefer M ′ to M outnumber those that prefer M to M ′. All stable matchings are popular and there is a simple linear time algorithm to compute a maximum-size popular matching. More generally, what we seek is a mi...