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An \(O(mn \log U)\) time algorithm for estimating the maximum cost of adjusting an infeasible network

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Abstract

This paper presents an \(O(mn \log U)\) time algorithm to solve the feasibility problem, where n, m and U are the number of nodes, arcs, and the value of maximum upper bound, respectively. The merit of this paper in comparison with maximum flow algorithms, is that it presents some information that is useful to modeler in estimating the maximum cost of adjusting the infeasible network. Our algorithm improves upon the previous \(O(mn \log (nU))\)-time method due to Ghiyasvand (Appl Math Modell 35:5276–5285, 2011). Also, the algorithm computes a feasible flow if the given network is feasible, but the method of Ghiyasvand (Appl Math Modell 35:5276–5285, 2011) does not compute a feasible flow if it is feasible.

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Acknowledgments

I thank the three anonymous reviewers for their constructive comments, which helped to improve the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Bu-Ali Sina University, Hamedan, Iran

    Mehdi Ghiyasvand

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  1. Mehdi Ghiyasvand
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Correspondence to Mehdi Ghiyasvand.

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Ghiyasvand, M. An \(O(mn \log U)\) time algorithm for estimating the maximum cost of adjusting an infeasible network. Telecommun Syst 63, 719–725 (2016). https://doi.org/10.1007/s11235-016-0151-9

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