Computing the Expected Values of some Properties of Randomly Weighted Graphs

Consider the setting of randomly weighted graphs, namely, graphs whose edge weights are independent discrete random variables with finite support over the non-negative reals. Given a randomly weighted graph G, we are interested in computing the expected values of various graph properties of G. In particular, we focus on the problem of computing the expected diameter of G. It is easy to show that this problem is #P-hard even in the restricted case in which all edge weights are identically distributed. In this paper we prove that this problem admits a fully polynomial time randomized approximation scheme (FPRAS). Our technique can also be used to derive an FPRAS for the problem of computing the expected weight of an MST of G