The mean field traveling salesman and related problems by Johan

In a complete graph on n vertices, the edges are assigned independent random costs from a fixed distribution μ on the non-negative real numbers. This is the mean field model of distance. Several well-known optimization problems consist in finding a set of edges of minimum total cost under certain constraints. Examples are minimum matching, spanning tree, and the traveling salesman problem (TSP). The distribution of the cost of the solution to these problems has been studied extensively, in particular when μ is either uniform on the interval [0, 1] or exponential of mean 1. These distributions both represent the so-called pseudo-dimension 1 case, in which a variable X of distribution μ satisfies P (X <t) t ! 1, as t! 0. (1)