Abstract
First, we give a detailed review of two algorithms that solve the minimization case of the assignment problem, the Bertsekas auction algorithm and the Goldberg & Kennedy algorithm. It was previously alluded that both algorithms are equivalent. We give a detailed proof that these algorithms are equivalent. Also, we perform experimental results comparing the performance of three algorithms for the assignment problem: the \(\epsilon \)-scaling auction algorithm, the Hungarian algorithm and the FlowAssign algorithm. The experiment shows that the auction algorithm still performs and scales better in practice than the other algorithms which are harder to implement and have better theoretical time complexity.
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This research was partially supported by SNI and CONACyT.
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Alfaro, C.A., Perez, S.L., Valencia, C.E. et al. The assignment problem revisited. Optim Lett 16, 1531–1548 (2022). https://doi.org/10.1007/s11590-021-01791-4
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DOI: https://doi.org/10.1007/s11590-021-01791-4