Popular and clan-popular b -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...

Popular b-matchings

In the paper we study popular b-matchings, which in other words are popular many-to-many matchings. The problem can be best described in graph terms: We are given a bipartite graph G = (A ∪H,E), a capacity function on vertices b : A ∪H → N and a rank function on edges r : E → N . A stands for the set of agents and H for the set of houses. Each member of a set of agents a ∈ A has a preference li...

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 ...