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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)

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)

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)

We consider two variants of the classical Stable Roommates problem with Incomplete (but strictly ordered) preference lists (sri) that are degree constrained, i.e., preference lists are of bounded length. The first variant, egal d-sri, involves finding an egalitarian stable matching in solvable instances of sri with preference lists of length at most d. We… (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 a many-to-many generalization of the well-known stable marriage problem, where we seek a bipartite assignment between, say, jobs (of varying sizes) and machines (of varying capacities) that is " stable " based on a set of underlying preference lists submitted by the jobs and machines. Building on the initial work of [6], we… (More)

Sciences to collaborate with´Agnes Cseh. As outlined in the proposal, we studied new and simplified algorithms for various stable flow problems. We were successful in obtaining 1. a polynomial-time augmenting path algorithm for computing a stable flow, 2. a simple algorithm for stable flows with restricted edges, which either computes a stable flow avoiding… (More)