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Algorithms 2013, 6(3), 532-545; doi:10.3390/a6030532

Stable Flows over Time

TU Berlin, Institut f¨ur Mathematik, Straße des 17. Juni 136, Berlin 10623, Germany
Author to whom correspondence should be addressed.
Received: 31 December 2012 / Revised: 27 July 2013 / Accepted: 9 August 2013 / Published: 21 August 2013
(This article belongs to the Special Issue Special Issue on Matching under Preferences)
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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 properties of stable flows over time on networks with an infinite time horizon. Finally, we discuss the influence of storage at vertices, with different results depending on the priority of the corresponding holdover edges.
Keywords: stable matchings; stable flows; flows over time stable matchings; stable flows; flows over time
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Cseh, Á.; Matuschke, J.; Skutella, M. Stable Flows over Time. Algorithms 2013, 6, 532-545.

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