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Baumann, Nadine ; Skutella, Martin

Computing earliest arrival flows with multiple sources

05361.SkutellaMartin.ExtAbstract.567.pdf (0.1 MB)


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.

BibTeX - Entry

  author =	{Nadine Baumann and Martin Skutella},
  title =	{Computing earliest arrival flows with multiple sources},
  booktitle =	{Algorithmic Aspects of Large and Complex Networks},
  year =	{2006},
  editor =	{Stefano Leonardi and Friedhelm Meyer auf der Heide and Dorothea Wagner},
  number =	{05361},
  series =	{Dagstuhl Seminar Proceedings},
  ISSN =	{1862-4405},
  publisher =	{Internationales Begegnungs- und Forschungszentrum f{\"u}r Informatik (IBFI), Schloss Dagstuhl, Germany},
  address =	{Dagstuhl, Germany},
  URL =		{},
  annote =	{Keywords: Networks, flows over time, dynamic flows, earliest arrival, evacuation}

Keywords: Networks, flows over time, dynamic flows, earliest arrival, evacuation
Seminar: 05361 - Algorithmic Aspects of Large and Complex Networks
Issue Date: 2006
Date of publication: 08.05.2006

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