ON THE RANDOM n×n ASSIGNMENT PROBLEM Lee, Sung-Chul; Zhonggen, Su;
Consider the random n m assignment problem with m Let be iid uniform random variables on [0, 1] and exponential random variables with mean 1, respectively, and let and denote the optimal assignment costs corresponding to and . In this paper we first give a comparison result about the discrepancy E -E . Using this comparison result with a known lower bound for Var( ) we obtains a lower bound for Var( ). Finally, we study the way that E and E vary as m does. It turns out that only when m - n is large enough, the cost decreases significantly.tly.