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Optimizing Cost Flows by Modifying Arc Costs and Capacities

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Graph-Theoretic Concepts in Computer Science (WG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1928))

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Abstract

We examine a network upgrade problem for cost flows. A budget can be distributed among the arcs of the network. An investment on a single arc can be used either to decrease the arc flow cost, or to increase the arc capacity, or both. The goal is to maximize the flow through the network while not exceeding bounds on the budget and on the total flow cost.

The problems are NP-hard even on series-parallel graphs. We provide an approximation algorithm on series-parallel graphs which, for arbitrary δ,ε > 0, produces a solution which exceeds the bounds on the budget and the flow cost by factors 1+δ and 1+ε, respectively, while the amount of flow is at least that of an optimum solution. The running time of the algorithm is polynomial in the input size and 1/(δε).

Supported by the Deutsche Forschungsgemeinschaft (DFG), Grant NO 88/15-3.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Würzburg, Am Hubland, 97074, Würzburg, Germany

    Ingo Demgensky, Hartmut Noltemeier & Hans-Christoph Wirth

Authors
  1. Ingo Demgensky
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  2. Hartmut Noltemeier
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  3. Hans-Christoph Wirth
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Editor information

Editors and Affiliations

  1. Department of Computer and Information Science, University of Konstanz, Box D 188, 78457, Konstanz, Germany

    Ulrik Brandes  & Dorothea Wagner  & 

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© 2000 Springer-Verlag Berlin Heidelberg

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Demgensky, I., Noltemeier, H., Wirth, HC. (2000). Optimizing Cost Flows by Modifying Arc Costs and Capacities. In: Brandes, U., Wagner, D. (eds) Graph-Theoretic Concepts in Computer Science. WG 2000. Lecture Notes in Computer Science, vol 1928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40064-8_12

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  • DOI: https://doi.org/10.1007/3-540-40064-8_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41183-3

  • Online ISBN: 978-3-540-40064-6

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