Weighted popular matchings

Weighted Random Popular Matchings

For a set A of n applicants and a set I of m items, let us consider the problem of matching applicants to items, where each applicant x ∈ A provides its preference list defined on items. We say that an applicant x prefers an item p than an item q if p is located at higher position than q in its preference list. For any matchingsM andM′ of the matching problem, we say that an applicant x prefers...

Popular Matchings

Popular matchings in the weighted capacitated house allocation problem

We consider the problem of finding a popular matching in the Weighted Capacitated House Allocation problem (WCHA). An instance of WCHA involves a set of agents and a set of houses. Each agent has a positive weight indicating his priority, and a preference list in which a subset of houses are ranked in strict order. Each house has a capacity that indicates the maximum number of agents who could ...

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 ...