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Complexity analysis for maximum flow problems with arc reversals

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Abstract

We provide a comprehensive study on network flow problems with arc reversal capabilities. The problem is to identify the arcs to be reversed in order to achieve a maximum flow from source(s) to sink(s). The problem finds its applications in emergency transportation management, where the lanes of a road network could be reversed to enable flow in the opposite direction. We study several network flow problems with the arc reversal capability and discuss their complexity. More specifically, we discuss the polynomial time algorithms for the maximum dynamic flow problem with arc reversal capability having a single source and a single sink, and for the maximum (static) flow problem. The presented algorithms are based on graph transformations and reductions to polynomially solvable flow problems. In addition, we show that the quickest transshipment problem with arc reversal capability and the problem of minimizing the total cost resulting from arc switching costs are \(\mathcal{NP}\) -hard.

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Authors and Affiliations

  1. Department of Industrial & Systems Engineering, Center for Applied Optimization, University of Florida, Gainesville, FL, 32611, USA

    Steffen Rebennack, Ashwin Arulselvan & Panos M. Pardalos

  2. Department of Civil & Coastal Engineering, Transportation Research Center, University of Florida, Gainesville, FL, 32611, USA

    Lily Elefteriadou

Authors
  1. Steffen Rebennack
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  2. Ashwin Arulselvan
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  3. Lily Elefteriadou
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  4. Panos M. Pardalos
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Corresponding author

Correspondence to Panos M. Pardalos.

Additional information

This research work was funded by UF Center for Multimodal solutions for Congestion Mitigation (CMS).

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Rebennack, S., Arulselvan, A., Elefteriadou, L. et al. Complexity analysis for maximum flow problems with arc reversals. J Comb Optim 19, 200–216 (2010). https://doi.org/10.1007/s10878-008-9175-8

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  • DOI: https://doi.org/10.1007/s10878-008-9175-8

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