Universally Maximum Ow with Piecewise-constant Capacities
نویسنده
چکیده
A maximum dynamic ow generalizes the standard maximum ow problem by introducing time. The object is to send as much ow from source to sink in T time units as possible. A related problem is the universally maximum ow, which asks to send a ow from source to sink that maximizes the amount of ow arriving at the sink by time t 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 ow that maximizes the amount of ow reaching the sink in all time intervals (0; t] for all 0 < t T, in O(k 2 mn log(kn 2 =m)) time. The best previous algorithm requires O(nk) maximum ow computations on a network with (m + n)k arcs and nk nodes.
منابع مشابه
Universally Maximum Flow with Piecewise-Constant Capacities
A maximum flow over time generalizes standard maximum flow by introducing a time component. 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 arri...
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