Multicommodity flows over time: Efficient algorithms and complexity
Theoretical Computer Science
Mathematics of Operations Research
The Maximum Energy-Constrained Dynamic Flow Problem
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Earliest Arrival Flows with Multiple Sources
Mathematics of Operations Research
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
An FPTAS for flows over time with aggregate arc capacities
WAOA'10 Proceedings of the 8th international conference on Approximation and online algorithms
Budget-constrained bulk data transfer via internet and shipping networks
Proceedings of the 8th ACM international conference on Autonomic computing
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
Generalized maximum flows over time
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Maximum multicommodity flows over time without intermediate storage
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Approximating earliest arrival flows in arbitrary networks
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Earliest arrival flows in networks with multiple sinks
Discrete Applied Mathematics
Hi-index | 0.00 |
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. Traditionally, flows over time are solved in time-expanded networks that 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. We present several approaches for coping with this difficulty. First, 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 length-bounded flows lead to provably good multicommodity flows over time. Second, we investigate “condensed” time-expanded networks which rely on a rougher discretization of time. 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, our approach yields fully polynomial-time approximation schemes for the NP-hard quickest min-cost and multicommodity flow problems. For single commodity problems, we show that storage of flow at intermediate nodes is unnecessary, and our approximation schemes do not use any.