We give a conjecture for the expected value of the optimal
k-assignment in an m times n matrix, where the entries are
all exp(1)-distributed random variables or zeros. This conjecture
generalizes a conjecture of Coppersmith and Sorkin. We prove this
conjecture for the case that there is a zero-cost
k-1-assignment. Assuming our conjecture, we determine some
limits, as k=m=n tends to infinity, of the expected cost of an
optimal n-assignment in an n by n matrix with zeros in a given
region. If we take the region outside a quarter-circle inscribed
in the square matrix, this limit is thus conjectured to be
Pi^2/24.
