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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)
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)
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 $$G= (A\, \dot{\cup }\, P, E)$$ 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)
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)
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)