Continuous-time flows in networks
Mathematics 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
Faster Algorithms for the Quickest Transshipment Problem
SIAM Journal on Optimization
Approximating earliest arrival flows with flow-dependent transit times
Discrete Applied Mathematics
SIAM Journal on Computing
Earliest Arrival Flows with Multiple Sources
Mathematics of Operations Research
Generalized maximum flows over time
WAOA'11 Proceedings of the 9th international conference on Approximation and Online Algorithms
Efficient continuous-time dynamic network flow algorithms
Operations Research Letters
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Hi-index | 0.00 |
The earliest arrival flow problem is motivated by evacuation planning. It asks for a flow over time in a network with supplies and demands that maximizes the satisfied demands at every point in time. Gale [1959] has shown the existence of such flows for networks with a single source and sink. For multiple sources and a single sink the existence follows from work by Minieka [1973] and an exact algorithm has been presented by Baumann and Skutella [FOCS '06]. If multiple sinks are present, it is known that earliest arrival flows do not exist in general. We address the open question of approximating earliest arrival flows in arbitrary networks with multiple sinks and present constructive approximations of time and value for them. We give tight bounds for the best possible approximation factor in most cases. In particular, we show that there is always a 2-value-approximation of earliest arrival flows and that no better approximation factor is possible in general. Furthermore, we describe an FPTAS for computing the best possible approximation factor (which might be better than 2) along with the corresponding flow for any given instance.