Abstract
An algorithm is given for solving the optimum potential problem, which is the dual of the classical “out-of-kilter” algorithm for flow problems. Moreover, a new proof of finiteness is provided, which holds even for non-rational data; it applies to all the algorithms of network theory which include a labeling process.
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References
L.R. Ford Jr. and D.R. Fulkerson,Flows in networks (Princeton University Press, Princeton, N.J., 1962).
D.R. Fulkerson, “An out-of-kilter method for minimal cost flow problems,”Journal of the Society for Industrial and Applied Mathematics 9 (1961) 18–27.
A. Ghouila-Houri, “Sur l'existence d'un flot ou d'une tension prenant ses valeurs dans un groupe abélien,”Comptes-Rendus de l'Académie des Sciences 250 (1960) 3931–3932.
B. Roy, “Contribution de la théorie des graphes à l'étude de certains problèmes linéaires”,Comptes-Rendus de l'Académie des Sciences 248 (1959) 2437–2439.
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Pla, JM. An “out-of-kilter” algorithm for solving minimum cost potential problems. Mathematical Programming 1, 275–290 (1971). https://doi.org/10.1007/BF01584092
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DOI: https://doi.org/10.1007/BF01584092