A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
A survey of dynamic network flows
Annals of Operations Research
Efficient dynamic network flow algorithms
Efficient dynamic network flow algorithms
Scheduling in synchronous networks and the greedy algorithm
Theoretical Computer Science
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
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
SIAM Journal on Computing
Efficient continuous-time dynamic network flow algorithms
Operations Research Letters
The impact of local policies on the quality of packet routing in paths, trees, and rings
Journal of Scheduling
The Maximum Energy-Constrained Dynamic Flow Problem
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Traffic Networks and Flows over Time
Algorithmics of Large and Complex Networks
Real-Time Message Routing and Scheduling
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Discrete Applied Mathematics
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Ad hoc solution of the multicommodity-flow-over-time problem
IEEE Transactions on Intelligent Transportation Systems
Maximum multicommodity flows over time without intermediate storage
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Computers and Industrial Engineering
Hi-index | 5.23 |
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.