Title
An FPTAS for Quickest Multicommodity Flows with
Inflow-Dependent Transit Times
Authors
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Publication
Submitted. An extended abstract appeared in S. Arora,
K. Jansen, J. D. P. Rolim, and A. Sahai, editors,
Approximation, Randomization, and Combinatorial
Optimization, Lecture Notes in Computer Science 2764,
Springer: Berlin, 2003, 71-82, Proceedings of the 6th
International Workshop on Approximation Algorithms for
Combinatorial Optimization Problems (APPROX'03).
Source
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Classification
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| MSC: |
| primary: | 90C27 | Combinatorial optimization |
| secondary: | 90B10 | Network models, deterministic |
| 90B20 | Traffic problems |
| 90C35 | Programming involving graphs or networks |
| 05C85 | Graph algorithms |
| 90C59 | Approximation methods and heuristics |
| 68W25 | Approximation algorithms |
| 68Q25 | Analysis of algorithms and problem complexity |
Keywords
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Approximation algorithms, dynamic flow, flow over time,
graph algorithms, network flow, routing, traffic models
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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 a fully polynomial
time approximation scheme (FPTAS) for the quickest multicommodity
flow problem with bounded cost.
