A survey of dynamic network flows
Annals of Operations Research
Approximation schemes for the restricted shortest path problem
Mathematics of Operations Research
The network inhibition problem
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Polynomial time algorithms for some evacuation problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
The Quickest Transshipment Problem
Mathematics of Operations Research
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
Minimum Cost Dynamic Flows: The Series-Parallel Case
Proceedings of the 4th International IPCO Conference on Integer Programming and Combinatorial Optimization
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Efficient continuous-time dynamic network flow algorithms
Operations Research Letters
A simple efficient approximation scheme for the restricted shortest path problem
Operations Research Letters
Approximately optimal control of fluid networks
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum cost flows over time without intermediate storage
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Time-Expanded Graphs for Flow-Dependent Transit Times
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Multicommodity flows over time: Efficient algorithms and complexity
Theoretical Computer Science
Mathematics of Operations Research
Scheduling algorithms for procrastinators
Journal of Scheduling
Earliest Arrival Flows with Multiple Sources
Mathematics of Operations Research
Traffic Networks and Flows over Time
Algorithmics of Large and Complex Networks
Multicommodity flows over time: efficient algorithms and complexity
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A Stackelberg strategy for routing flow over time
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Paths of bounded length and their cuts: Parameterized complexity and algorithms
Discrete Optimization
Static routing in symmetric real-time network-on-chips
Proceedings of the 20th International Conference on Real-Time and Network Systems
Maximum multicommodity flows over time without intermediate storage
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Traditionally, flows over time are solved in time-expanded networks which contain one copy of the original network for each discrete time step. While this method makes available the whole algorithmic toolbox developed for static flows, its main and often fatal drawback is the enormous size of the time-expanded network. In particular, this approach usually does not lead to efficient algorithms with running time polynomial in the input size since the size of the time-expanded network is only pseudo-polynomial.We present two different approaches for coping with this difficulty. Firstly, inspired by the work of Ford and Fulkerson on maximal s-t-flows over time (or 'maximal dynamic s-t-flows'), we show that static, lengthbounded flows lead to provably good multicommodity flows over time.These solutions not only feature a simple structure but can also be computed very efficiently in polynomial time.Secondly, we investigate 'condensed' time-expanded networks which rely on a rougher discretization of time. Unfortunately, there is a natural tradeoff between the roughness of the discretization and the quality of the achievable solutions. However, we prove that a solution of arbitrary precision can be computed in polynomial time through an appropriate discretization leading to a condensed time expanded network of polynomial size. In particular, this approach yields a fully polynomial time approximation scheme for the quickest multicommodity flow problem and also for more general problems.