Learn More
We are given a bipartite graph G = (A ∪ B, E) where each vertex has a preference list ranking its neighbors: in particular, every a ∈ A ranks its neighbors in a strict order of preference, whereas the preference lists of b ∈ B may contain ties. A matching M is popular if there is no matching M such that the number of vertices that prefer M to M exceeds the(More)
We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph G = (A ˙ ∪P, E) with weights on the edges in E, and with lower and upper quotas on the vertices in P. We seek a maximum weight many-to-one matching satisfying two sets of constraints: vertices in A are incident to at most one(More)
In this paper, the notion of stability is extended to network flows over time. As a useful device in our proofs, we present an elegant preflow-push variant of the Gale-Shapley algorithm that operates directly on the given network and computes stable flows in pseudo-polynomial time both in the static flow and the flow over time case. We show periodical(More)
Given a bipartite graph G = (A ∪ B, E) with strict preference lists and e * ∈ E, we ask if there exists a popular matching in G that contains the edge e *. We call this the popular edge problem. A matching M is popular if there is no matching M such that the vertices that prefer M to M outnumber those that prefer M to M. It is known that every stable(More)
We study a natural generalization of the maximum weight many-to-one matching problem. We are given an undirected bipartite graph $$G= (A\, \dot{\cup }\, P, E)$$ G = ( A ∪ ˙ P , E ) with weights on the edges in E, and with lower and upper quotas on the vertices in P. We seek a maximum weight many-to-one matching satisfying two sets of constraints: vertices(More)
The stable allocation problem is one of the broadest extensions of the well-known stable marriage problem. In an allocation problem , edges of a bipartite graph have capacities and vertices have quotas to fill. Here we investigate the case of uncoordinated processes in stable allocation instances. In this setting, a feasible allocation is given and the aim(More)
In the Stable Marriage and Roommates problems, a set of agents is given, each of them having a strictly ordered preference list over some or all of the other agents. A matching is a set of disjoint pairs of mutually acceptable agents. If any two agents mutually prefer each other to their partner, then they block the matching, otherwise, the matching is said(More)