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 cos...

In [1] it is shown that the rst order theory of almost all generalized Steinhaus graphs is identical to the rst order theory of almost all graphs where each generalized Steinhaus graph is given the same probability. A natural probability measure on generalized Steinhaus graphs is obtained by independently assigning a probability o f p for each entry in the generating string of the graph. With t...