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Solving Evacuation Problems Efficiently: Earliest Arrival Flows with Multiple Sources
Zitatschlüssel Report-035-2008
Autor Nadine Baumann and Martin Skutella
Jahr 2008
Nummer 035
Notiz Submitted. An extended abstract appeared in Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06), 339-408, 2006.
Institution Technische Universität Berlin, Institut für Mathematik
Zusammenfassung Earliest arrival flows capture the essence of evacuation planning. 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 for many years. We present an exact algorithm for this problem whose running time is strongly polynomial in the input plus output size of the problem.
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