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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)

Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems – streets, tracks, etc. – are inherently undirected and directions are only imposed on them to reduce the danger of colliding vehicles and similar problems. Thus the question arises, what influence the orientation of the network has on the… (More)

Multi-commodity flows over time exhibit the non-intuitive property that letting flow wait can allow us to send flow faster overall. Fleischer and Skutella (IPCO 2002) show that the speed-up through storage is at most a factor of 2, and that there are instances where the speed-up is as large as a factor of 4/3. We close this gap by presenting a family of… (More)

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