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キーワード:
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要旨:
Given a network with capacities and transit times on the arcs, the
quickest flow problem asks for a `flow over time' that satisfies
given demands within minimal time. In the setting of flows over
time, flow on arcs may vary over time and the transit time of an arc
is the time it takes for flow to travel through this arc. In most
real-world applications (such as, e.g., road traffic, communication
networks, production systems, etc.), transit times are not fixed but
depend on the current flow situation in the network. We consider
the model where the transit time of an arc is given as a
nondecreasing function of the rate of inflow into the arc. We prove
that the quickest $s$-$t$-flow problem is NP-hard in this setting
and give various approximation results, including an FPTAS for the
quickest multicommodity flow problem with bounded cost.
