Minimal envy and popular matchings

Popular Matchings

Popular and Clan-Popular b-Matchings

Suppose that each member of a set of agents has a preference list of a subset of houses, possibly involving ties, and each agent and house has their capacity denoting the maximum number of houses/agents (respectively) that can be matched to him/her/it. We want to find a matching M , called popular, for which there is no other matching M ′ such that more agents prefer M ′ to M than M to M ′, sub...

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...

Popular Matchings: Structure and Algorithms

An instance of the popular matching problem (POP-M) consists of a set of applicants and a set of posts. Each applicant has a preference list that strictly ranks a subset of the posts. A matching M of applicants to posts is popular if there is no other matching M ′ such that more applicants prefer M ′ to M than prefer M to M . Abraham et al [1] described a linear time algorithm to determine whet...

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 ...