Mathematical Equivalence of the Auction Algorithm for Assignment and the ∊-Relaxation (Preflow-Push) Method for Min Cost Flow

Dimitri P. Bertsekas
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Dimitri P. Bertsekas: M J.T, Laboratory for Information and Decision Systems

A chapter in Large Scale Optimization, 1994, pp 26-44 from Springer

Abstract: 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.

Keywords: Assignment Problem; Price Vector; Similarity Class; Minimum Cost Flow; Feasible Assignment (search for similar items in EconPapers)
Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4613-3632-7_2

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DOI: 10.1007/978-1-4613-3632-7_2

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