Scheduling to minimize average completion time: off-line and on-line algorithms
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Polynomial time algorithms for some evacuation problems
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Flows over time with load-dependent transit times
SODA '02 Proceedings of the thirteenth 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
Flows in Networks
Traffic Networks and Flows over Time
Algorithmics of Large and Complex Networks
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
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For the earliest arrival flow problem one is given a network G=(V,A) with capacities u(a) and transit times @t(a) on its arcs a@?A, together with a source and a sink vertex s,t@?V. The objective is to send flow from s to t that moves through the network over time, such that for each time @q@?[0,T) the maximum possible amount of flow up to this time reaches t. If, for each @q@?[0,T), this flow is a maximum flow for time horizon @q, then it is called earliest arrival flow. In practical applications a higher congestion of an arc in the network often implies a considerable increase in transit time. Therefore, in this paper we study the earliest arrival problem for the case that the transit time of each arc in the network at each time @q depends on the flow on this particular arc at that time @q. For constant transit times it has been shown by Gale that earliest arrival flows exist for any network. We give examples, showing that this is no longer true for flow-dependent transit times. For that reason we define a relaxed version of this problem where the objective is to find flows that are almost earliest arrival flows. In particular, we are interested in flows that, for each @q@?[0,T), need only @a-times longer to send the maximum flow to the sink. We give both constant lower and upper bounds on @a; furthermore, we present a constant factor approximation algorithm for this problem.