A survey of dynamic network flows
Annals of Operations Research
Efficient dynamic network flow algorithms
Efficient dynamic network flow algorithms
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
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
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
Approximating earliest arrival flows with flow-dependent transit times
Discrete Applied Mathematics
Multicommodity flows over time: Efficient algorithms and complexity
Theoretical Computer Science
Scheduling algorithms for procrastinators
Journal of Scheduling
Traffic Networks and Flows over Time
Algorithmics of Large and Complex Networks
Uniform resource networks I. Complete graphs
Automation and Remote Control
Equilibria in Dynamic Selfish Routing
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
Multicommodity flows over time: efficient algorithms and complexity
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Asymmetrical resource networks. I. Stabilization processes for low resources
Automation and Remote Control
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
Generalized maximum flows over time
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
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Flows over time (also called dynamic flows) generalize standard network flows by introducing an element of time. They naturally model problems where travel and transmission are not instantaneous. Solving these problems raises issues that do not arise in standard network flows. One issue is the question of storage of flow at intermediate nodes. In most applications (such as, e.g., traffic routing, evacuation planning, telecommunications etc.), intermediate storage is limited, undesired, or prohibited.The minimum cost flow over time problem is NP-hard. In this paper we 1) prove that the minimum cost flow over time never requires storage; 2) provide the first approximation scheme for minimum cost flows over time that does not require storage; 3) provide the first approximation scheme for minimum cost flows over time that meets hard cost constraints, while approximating only makespan.Our approach is based on a condensed variant of time- expanded networks. It also yields fast approximation schemes with simple solutions for the quickest multicommodity flow problem.Finally, using completely different techniques, we describe a very simple capacity scaling FPAS for the minimum cost flow over time problem when costs are proportional to transit times. The algorithm builds upon our observation about the structure of optimal solutions to this problem: they are universally quickest flows. Again, the FPAS does not use intermediate node storage. In contrast to the preceding algorithms that use a time-expanded network, this FPAS runs directly on the original network.