Computing earliest arrival flows with multiple sources

Authors Nadine Baumann, Martin Skutella

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Nadine Baumann
Martin Skutella

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Nadine Baumann and Martin Skutella. Computing earliest arrival flows with multiple sources. In Algorithmic Aspects of Large and Complex Networks. Dagstuhl Seminar Proceedings, Volume 5361, pp. 1-3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)


Earliest arrival flows are motivated by applications related to evacuation. Given a network with capacities and transit times on the arcs, a subset of source nodes with supplies and a sink node, the task is to send the given supplies from the sources to the sink "as quickly as possible". The latter requirement is made more precise by the earliest arrival property which requires that the total amount of flow that has arrived at the sink is maximal for all points in time simultaneously. It is a classical result from the 1970s that, for the special case of a single source node, earliest arrival flows do exist and can be computed by essentially applying the Successive Shortest Path Algorithm for min-cost flow computations. While it has previously been observed that an earliest arrival flow still exists for multiple sources, the problem of computing one efficiently has been open. We present an exact algorithm for this problem whose running time is strongly polynomial in the input plus output size of the problem.
  • Networks
  • flows over time
  • dynamic flows
  • earliest arrival
  • evacuation


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