A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A fast parametric maximum flow algorithm and applications
SIAM Journal on Computing
A survey of dynamic network flows
Annals of Operations Research
Continuous-time flows in networks
Mathematics of Operations Research
An algorithm for a class of continuous linear programs
SIAM Journal on Control and Optimization
Efficient dynamic network flow algorithms
Efficient dynamic network flow algorithms
“The quickest transshipment problem”
Proceedings of the sixth 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
Faster algorithms for the quickest transshipment problem with zero transit times
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
A Study of General Dynamic Network Programs with Arc Time-Delays
SIAM Journal on Optimization
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The maximum dynamic flow problem generalizes the standard maximum flow problem by introducing time. The object is to send as much flow from source to sink in T time units as possible, where capacities are interpreted as an upper bound on the rate of flow entering an arc. A related problem is the universally maximum flow, which is to send a flow from source to sink that maximizes the amount of flow arriving at the sink by time t simultaneously for all t ≤ T. We consider a further generalization of this problem that allows arc and node capacities to change over time. In particular, given a network with arc and node capacities that are piecewise constant functions of time with at most k breakpoints, and a time bound T, we show how to compute a flow that maximizes the amount of flow reaching the sink in all time intervals (0, t] simultaneously for all 0 t ≤ T, in O(k2mn log(kn2/m)) time. The best previous algorithm requires O(nk) maximum flow computations on a network with (m+ n)k arcs and nk nodes.