On the expected value of the minimum assignment

The minimum k‐assignment of an m × n matrix X is the minimum sum of k entries of X, no two of which belong to the same row or column. Coppersmith and Sorkin conjectured that if X is generated by choosing each entry independently from the exponential distribution with mean 1, then the expected value of its minimum k‐assignment is given by an explicit formula, which has been proven only in a few cases. In this paper we describe our efforts to prove the Coppersmith–Sorkin conjecture by considering the more general situation where the entries xij of X are chosen independently from different distributions. In particular, we require that xij be chosen from the exponential distribution with mean 1/ricj. We conjecture an explicit formula for the expected value of the minimum k‐assignment of such X and give evidence for this formula. © 2002 Wiley Periodicals, Inc. Random Struct. Alg., 21: 33–58, 2002