Asymptotics in the random assignment problem
نویسنده
چکیده
In the deterministic assignment problem, there are n jobs, n machines and a n x n non-negative matrix (t j,,,) representing the cost of performing job j on machine m. An assignment is a permutation ~ of {1, ..., n}, indicating that job j is assigned to machine ~(j). The optimal assignment has cost min~tj ,~(j) , j the minimum taken over permutations re. For the random assignment problem we define the t j,,, to be independent r.v.'s with exponential distribution with mean n:
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