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Flow Increment through Network Expansion

Author

Listed:
  • Adrian Marius Deaconu

    (Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brasov, 50003 Brasov, Romania)

  • Luciana Majercsik

    (Department of Mathematics and Computer Science, Faculty of Mathematics and Computer Science, Transilvania University of Brasov, 50003 Brasov, Romania)

Abstract

The network expansion problem is a very important practical optimization problem when there is a need to increment the flow through an existing network of transportation, electricity, water, gas, etc. In this problem, the flow augmentation can be achieved either by increasing the capacities on the existing arcs, or by adding new arcs to the network. Both operations are coming with an expansion cost. In this paper, the problem of finding the minimum network expansion cost so that the modified network can transport a given amount of flow from the source node to the sink node is studied. A strongly polynomial algorithm is deduced to solve the problem.

Suggested Citation

  • Adrian Marius Deaconu & Luciana Majercsik, 2021. "Flow Increment through Network Expansion," Mathematics, MDPI, vol. 9(18), pages 1-9, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2308-:d:638616
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    References listed on IDEAS

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    1. Zhao Zhang & Xiaohui Huang, 2019. "Discrete Newton Method," Springer Optimization and Its Applications, in: Ding-Zhu Du & Panos M. Pardalos & Zhao Zhang (ed.), Nonlinear Combinatorial Optimization, pages 37-56, Springer.
    2. James B. Orlin, 1993. "A Faster Strongly Polynomial Minimum Cost Flow Algorithm," Operations Research, INFORMS, vol. 41(2), pages 338-350, April.
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