Random Assignment with Integer Costs

@article{Parviainen2004RandomAW,
  title={Random Assignment with Integer Costs},
  author={Robert Parviainen},
  journal={Combinatorics, Probability & Computing},
  year={2004},
  volume={13},
  pages={103-113}
}
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 n, and random permutations of 1, 2, . . . , n for each row, or of 1, 2, . . . , n for the whole matrix. We find the limit of the expected cost for the n cases, and prove bounds for the n cases. This is done by simple coupling arguments… CONTINUE READING