Random Assignment with Integer Costs

The random assignment problem is to minimize the cost of an assignment in a n×n matrix of random costs. In this paper we study this problem for some integer valued cost distributions. We consider both uniform distributions on 1, 2, . . . , m, for m = n or n2, and random permutations of 1, 2, . . . , n for each row, or of 1, 2, . . . , n2 for the whole matrix. We find the limit of the expected cost for the “n2” cases, and prove bounds for the “n” cases. This is done by simple coupling arguments together with Aldous recent results for the continuous case. We also present a simulation study of these cases.

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