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A Novel Dual Ascent Algorithm for Solving the Min-Cost Flow Problem

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2016

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Becker, Ruben
Fickert, Maximilian

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https://doi.org/10.1137/1.9781611974317.13
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GOODRICH, Michael, ed., Michael MITZENMACHER, ed.. 2016 Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments (ALENEX). Philadelphia: Siam, 2016, pp. 151-159. ISBN 978-1-61197-431-7. Available under: doi: 10.1137/1.9781611974317.13

Zusammenfassung

We present a novel algorithm for the min-cost flow problem that is competitive with recent third-party implementations of well-known algorithms for this problem and even outperforms them on certain realistic instances. We formally prove correctness of our algorithm and show that the worst-case running time is in O(‖b‖1(m + n log n)) where b is the vector of demands. Combined with standard scaling techniques, this pseudo-polynomial bound can be made polynomial in a straightforward way. Furthermore, we evaluate our approach experimentally. Our empirical findings indeed suggest that the running time does not significantly depend on the costs and that a linear dependence on ‖b‖1 is overly pessimistic.

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004 Informatik

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ALENEX16 : Meeting on Algorithm Engineering & Experiments, 10. Jan. 2016 - 10. Jan. 2016, Arlington, Virginia, USA
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ISO 690BECKER, Ruben, Maximilian FICKERT, Andreas KARRENBAUER, 2016. A Novel Dual Ascent Algorithm for Solving the Min-Cost Flow Problem. ALENEX16 : Meeting on Algorithm Engineering & Experiments. Arlington, Virginia, USA, 10. Jan. 2016 - 10. Jan. 2016. In: GOODRICH, Michael, ed., Michael MITZENMACHER, ed.. 2016 Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments (ALENEX). Philadelphia: Siam, 2016, pp. 151-159. ISBN 978-1-61197-431-7. Available under: doi: 10.1137/1.9781611974317.13
BibTex
@inproceedings{Becker2016Novel-34517,
  year={2016},
  doi={10.1137/1.9781611974317.13},
  title={A Novel Dual Ascent Algorithm for Solving the Min-Cost Flow Problem},
  isbn={978-1-61197-431-7},
  publisher={Siam},
  address={Philadelphia},
  booktitle={2016 Proceedings of the Eighteenth Workshop on Algorithm Engineering and Experiments (ALENEX)},
  pages={151--159},
  editor={Goodrich, Michael and Mitzenmacher, Michael},
  author={Becker, Ruben and Fickert, Maximilian and Karrenbauer, Andreas}
}
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