Abstract
It is well known that the linear minimum cost flow network problem can be converted to an equivalent assignment problem. Here we give a simple proof that when the auction algorithm is applied to this equivalent problem, one obtains the generic form of the ∊-relaxation method, and as a special case, the Goldberg-Tarjan preflow-push max-flow algorithm. The reverse equivalence is already known, that is, if we view the assignment problem as a special case of a minimum cost flow problem and we apply the ∊-relaxation method with some special rules for choosing the node to iterate on, we obtain the auction algorithm. Thus, the two methods are mathematically equivalent.
Research supported by NSF under Grant No. CCR-9103804, and by the ARO under Grant DAAL03-92-G-0115.
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© 1994 Kluwer Academic Publishers
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Bertsekas, D.P. (1994). Mathematical Equivalence of the Auction Algorithm for Assignment and the ∊-Relaxation (Preflow-Push) Method for Min Cost Flow. In: Hager, W.W., Hearn, D.W., Pardalos, P.M. (eds) Large Scale Optimization. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3632-7_2
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DOI: https://doi.org/10.1007/978-1-4613-3632-7_2
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