  In the traveling salesman problem, one must find the length of the shortest
closed tour visiting given ``cities''. We study the stochastic version of the
problem, taking the locations of cities and the distances separating them to be
random variables drawn from an ensemble. We consider first the ensemble where
cities are placed in Euclidean space. We investigate how the optimum tour
length scales with number of cities and with number of spatial dimensions. We
then examine the analytical theory behind the random link ensemble, where
distances between cities are independent random variables. Finally, we look at
the related geometric issue of nearest neighbor distances, and find some
remarkable universalities.
