Summary
We show that, in the usual probabilistic model for the random assignment problem, the optimal cost tends to a limit constant in probability and in expectation. The method involves construction of an infinite limit structure, in terms of which the limit constant is defined. But we cannot improve on the known numerical bounds for the limit.
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Research supported by NSF Grant MCS90-01710
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Aldous, D. Asymptotics in the random assignment problem. Probab. Th. Rel. Fields 93, 507–534 (1992). https://doi.org/10.1007/BF01192719
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DOI: https://doi.org/10.1007/BF01192719