A survey of dynamic network flows
Annals of Operations Research
Efficient dynamic network flow algorithms
Efficient dynamic network flow algorithms
The Quickest Transshipment Problem
Mathematics of Operations Research
Minimum cost flows over time without intermediate storage
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum Cost Dynamic Flows: The Series-Parallel Case
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Quickest Multicommodity Flow Problem
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Call Scheduling in Trees, Rings and Meshes
HICSS '97 Proceedings of the 30th Hawaii International Conference on System Sciences: Software Technology and Architecture - Volume 1
Efficient continuous-time dynamic network flow algorithms
Operations Research Letters
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Universal packet routing with arbitrary bandwidths and transit times
IPCO'11 Proceedings of the 15th international conference on Integer programming and combinatoral optimization
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Packet routing: complexity and algorithms
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
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Flow variation over time is an important feature in network flow problems arising in various applications such as road or air traffic control, production systems, communication networks (e.g., the Internet), and financial flows. The common characteristic are networks with capacities and transit times on the arcs which specify the amount of time it takes for flow to travel through a particular arc. Moreover, in contrast to static flow problems, flow values on arcs may change with time in these networks. While the 'maximum s-t-flow over time' problem can be solved efficiently and 'min-cost flows over time' are known to be NP-hard, the complexity of (fractional) 'multicommodity flows over time' has been open for many years. We prove that this problem is NP-hard, even for series-parallel networks, and present new and efficient algorithms under certain assumptions on the transit times or on the network topology. As a result, we can draw a complete picture of the complexity landscape for flow over time problems.