An FPTAS for flows over time with aggregate arc capacities

Authors:
Daniel Dressler;Martin Skutella
Affiliations:
Institute for Mathematics, TU Berlin, Berlin, Germany;Institute for Mathematics, TU Berlin, Berlin, Germany
Venue:
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Year:
2010

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Abstract

We study flows over time in networks with transit times on the arcs. Transit times describe how long it takes to traverse an arc. A flow over time specifies for each arc a time-dependent flow rate that must always be bounded by the arc's capacity. Only recently, Melkonian introduced an alternative model where so-called bridge capacities bound the total amount of flow traveling along an arc, at any point of time. The contribution of this paper is twofold. Firstly, we introduce a common generalization of both the classical flow over time model and Melkonian's model. Secondly, we present a non-trivial extension of an FPTAS by Fleischer and Skutella to our new flow model. Prior to this, no approximation algorithm was known for Melkonian's model.